Tension control of fasteners

ABSTRACT

There is disclosed a technique for tightening threaded fasteners in which values of offset torque, initial tension rate relative to angle, final tension rate relative to angle and other joint related factors are empirically determined by instrumenting a plurality of fasteners of the type ultimately to be tightened. In one embodiment, torque and angle are monitored during tightening. Calculations are conducted, while tightening, to determine the tension prevailing in the bolt at a particular angle of advance. By using the calculated tension value and the particular angle of advance, an instantaneous position of threading advance on the tension-angle curve of the fastener is established. From this instantaneous position, it is determined how much greater angle of advance or how much torque is required to tighten the fasteners to a final desired tension value. The same technique may also be used merely to monitor tightening which is terminated by a different tightening strategy. A number of quality control procedures are conducted to determine if the fastener and the tightening tool are performing normally. In another embodiment, analog devices are utilized to convert sensed values of torque and the rate of threading advance into parameters which control tool shut off.

This is a division, of application Ser. No. 912,151, filed June 2, 1978,U.S. Pat. No. 4,179,786, which was a continuation-in-part of applicationSer. No. 712,554, filed Aug. 9, 1976, now abandoned. and of applicationSer. No. 766,429, filed Feb. 7, 1977, U.S. Pat. No. 4,106,570.

This invention relates to technique for tightening threaded fasteners.The function of threaded fasteners is, of course, to unite two or morepieces into a typically rigid part called a joint. For purposes ofconvenience, the term fastener pair may be used to designate male andfemale threaded members, e.g. a nut and bolt, bolt and internallythreaded hole of a joint part, threaded stud and nut, and the like. Theconnected pieces of a joint should be so tightened as to remain incontact during vibration, static and/or dynamic loading of the part, andthe like. In many applications where several threaded fasteners areused, it may be of substantial importance to assure that the contactpressure between the pieces created by the fasteners is uniform sincenon-uniform deflection of the pieces may create unacceptable jointconditions. Proper assembly should produce uniform contact pressuresfrom joint to joint in accordance with design requirements. This can beachieved only by assembly procedures that produce uniform joint preloador clamping load. Although it is conceivable to determine joint preloador clamping load in terms of compression of a nut, it is more practicalto deal in terms of bolt tension. There is, unfortunately, no directtechnique for measuring bolt load externally without instrumenting thebolt or using a load washer which is either impractical or uneconomicfor assembly line production. Accordingly, all practical techniques ofbolt tension control in production quantities are inferential.

There are a number of well known techniques for tightening threadedfasteners based on information available from external instruments suchas torque and angles sensors as contrasted to specially designedfasteners or load washers. Included in these techniques are torquecontrol, turn-of-the-nut method, the yield point method, acousticmeasuring, overrunning schemes and torque rate methods.

One of the present techniques in wide use is torque control in which aconstant final torque is applied to all fasteners. Final torque istypically produced by a stall air tool and the degree of torque controldepends on the uniformity of air pressure, motor performance and thehardness of the joint. The intention is to achieve tension scatters inthe range of +10-20% about the mean. The actual scatter limits can beverified by instrumenting the bolts in a laboratory environment.Opinions vary on what tension scatters are actually present in largequantities of fasteners tightening with torque control method. It wouldnot be surprising to learn that total tension scatter in productionquantities is on the order of ±100% of mean which can be caused by a±41% scatter in friction alone.

Torque is, of course, related to tension but the relationship is subjectto large uncertanties resulting from a first order dependence on threadand head friction. In the simplest theoretical consideration, thefollowing equation describes the relation of torque and tension:

    T=(f.sub.h r.sub.h +f.sub.th r.sub.th)F                    (1)

where T is torque, f_(h) is the coefficient of friction between thefastener head and the abutting piece, r_(h) is the effective radius ofhead friction, f_(th) is the coefficient of friction between the threadsof the fastener, r_(th) is the effective radius of thread friction and Fis bolt tension. Although the mean value of the coefficients of frictioncan be substantially reduced by lubricants and coatings, the relativescatter about the mean value cannot be substantially affected. Combiningthe friction uncertainties with the variations in applied torque, thetension control actually achieved in practice is quite poor.Accordingly, in order to minimize fastener failure during assembly, themeans torque must be designed at unreasonably low levels as comparedwith the strength of the bolt. Even with unreasonably low mean torquevalues, a significant proportion of the fasteners are woefullyunderstressed while many have been stressed past the elastic limit.

Discussions of torque control methods of tightening threaded fastenersare found in Assembly Engineering, October 1966, pages 24-29;Hydrocarbon Processing, Jan. 1973, pages 89-91; Machine Design, Mar. 6,1975, pages 78-82; The Engineer, London, May 26, 1967, pages 770-71,Iron Age, Feb. 24, 1966, page 66; Machine Design, Feb. 13, 1964, pages108-85; Power Engineering, Oct. 1963, page 58; and U.S. Pat. Nos.3,555,938 and 3,851,386.

Another widely used technique for tightening threaded fasteners inproduction quantities is called the turn-of-the-nut method which makesuse of the applied torque as well as the angle of threaded advance. Inits simplest form, the technique is to advance the fasteners until apredetermined torque value is reached, for example snug torque, and thenturn each nut an additional constant predetermined angle. The concept isthat the relation of the turn of the fastener to the strain of the boltwill eliminate the influence of friction on the final desired tensionvalue. If the clamped pieces were purely elastic and contact betweenthem were immediate and perfect, one would expect the bolt tension toincrease linearly with unit angle of advance starting with the value ofzero at the onset of contact. In theory, tension control would be asaccurate as the uniformity of the joint tension rate which is the slopeof the curve obtained by plotting tension against angle of advance.

In practice, the tension rate is not exactly a constant from joint tojoint nor is it uniform as a function of angle for any single joint. Thereasons are related to microplasticity which is the yield of surfaceirregularities in the moving fastener components, lubricant squeeze filmand the fact that contact is gradual rather than immediate. Theturn-of-the-nut method is customarily considered to be substantiallysuperior to the torque control technique although data developed duringthe investigation of this invention suggests that this method issubstantially overrated, at least at low to moderate tension values. Theturn-of-the-nut method does have the disadvantage of partly relying ontorque which is subject to the large uncertainties previously discussed.The selection of the threshold torque is a critical decision. Ifthreshold torque is too high, the theoretical advantage over the torquecontrol method is substantially reduced. If threshold torque is too low,final bolt tension will fluctuate greatly from joint to joint, since atlow torque values, both the torque-angle and the tension angle curveshave varying curvature. The combination of uncertain tension at thethreshold torque and nonuniformity of tension rate in a large angle spanwill more than offset the theoretical advantage gained. Theturn-of-the-nut method, being essentially a strain approach totightening, has the advantage of reducing substantially the rate of boltfailure during assembly because very large strains can be sustained bythe bolt material in the plastic zone. During the investigation of thisinvention it has been learned that the difference between low torquerate fasteners and high torque rate fasteners from the same sample candevelop a scatter in the final desired tension value of ±50% at tensionvalues in the range of 3000 pounds for a 5/16"-24, grade 8, bolt usingthe turn-of-the-nut method. As the final tension value increases, thescatter reduces as a percentage of final tension.

Another difficulty with turn-of-the-nut methods is that recalibration isrequired when the final desired tension value is changed. This is incontrast to this invention where the final desired tension value can bechanged at will so long as this value is in the second tension raterange and is sufficiently far from the break in the tension curve sothat the tool will not run past the desired value because of tooloverrun.

Discussion of turn-of-the-nut methods of tightening threaded fastenersare found in Hydrocarbon Processing, Jan. 1973, pages 89-91; MachineDesign, Mar. 6, 1975, pages 78-82; Journal of the Structural Division,Processings of the American Society of Civil Engineers, April 1966,pages 20-40; Machine Design, Feb. 13, 1964, pages 180-85; and U.S. Pat.No. 3,851,386.

As pointed out in some detail in U.S. Pat. Nos. 3,643,501; 3,963,726;3,965,778; 3,973,434; 3,974,883; 3,982,419; 4,000,782; and 4,008,772;and Design Engineering (London), January 1975, pages 21-23, 25, 27, 29,another approach for tightening threaded fasteners is known as the yieldpoint method. In this approach, an attempt is made during tightening tosense the onset of plastic elongation of the bolt and terminatetightening in response thereto. The yield point, which is the boundarybetween the elastic and plastic deformation zones of a metal in auniaxial state of stress, is quite difficult to determine precisely.Accordingly, the yield point is often defined in terms of an offsetstrain, typically 0.1-0.2%, which is arbitrarily chosen.

It is apparent that a joint is made up of the clamped pieces as well asthe fasteners. The design is usually such that yielding occurs in thebolt shank although it could conceivably occur in the bolt head or nut.The bolt is also subject to shear as a result of torsion created by theturning moment or torque. Accordingly, a bolt is in a combined state ofstress. Thus, at high torque values, the stress in the bolt is due toboth torque and tension and can substantially alter the tensile strengthof a particular specimen. Additional errors may be introduced when thegoal is bolt tension control due to natural scatters in the materialyield point. Other errors involved in yield point methods are the resultof noise in the torque signal and other uncertainties in consistentlysensing the yield point. The main objection to the yield point method isthe concern over the fatigue strength and reusability of the bolt.Although the matter is subject to some controversy, it appears clearthat one time application and release of an external load will causerelaxation of the joint and accordingly reduce the clamping forceapplied by the bolt below the original clamping force. In extreme case,the bolt may lose all tension and be loose.

Other techniques related to yield point methods are found in U.S. Pat.Nos. 3,939,920 and 3,974,685. In the former, the technique basically isto measure a tightening parameter, e.g. torque, at the yield point,conduct certain calculations and back off the nut until the finaldesired axial stress is achieved and terminate tightening. In thelatter, the technique is to provide a washer which yields at a knownstress value below the yield point of the bolt. When the washer yields,a torque value is obtained and noted at a known stress value.Extrapolations are made to obtain a calculated torque value at a desiredelevated stress value in the bolt. Tightening is terminated in responseto the calculated torque value.

An overrunning approach which may be used to detect galled threads orcross threaded members is disclosed in U.S. Pat. Nos. 3,368,396 and3,745,820. In this technique, a warning signal is generated when apredetermined torque is developed before a given number of turns hasbeen effected which may be indicative of galled threads. A differentwarning signal is generated when a larger number of turns are effectedbefore the development of a desired higher torque is obtained which issuggestive of cross threading. It will be apparent that these approachesare not designed to control bolt tension.

Another approach for controlling bolt tension involves acoustic deviceswhich attempt to measure the elongation in a bolt caused by tension.Such devices are discussed and illustrated in U.S. Pat. Nos. 3,306,100;3,307,393; 3,650,016; 3,759,090 and 3,822,587.

Another group of prior art techniques which has been suggested involve aconsideration of the rate of torque increase relative to the angle ofthreading advance as disclosed in Assembly Engineering, September 1974,pages 42-45; Design Engineering (London), January 1975, pages 21-23, 25,27, 29; Iron Age, Apr. 28, 1975, page 44; and Machine Design, Volume 47,Jan. 23, 1975, page 44. These techniques monitor the torque-angle curveduring tightening in order to terminate tightening in response toconclusions derived from the torque-angle relationship. In the DesignEngineering disclosure, tightening is terminated upon sensing asignificant drop in the torque rate, which occurs at the yield point. Inthe remaining articles, tightening is apparently terminated when apredetermined torque range is attained within a fairly narrow anglerange. These disclosures are thus similar to the overrunning schemesmentioned above.

The goal of inferential tightening techniques is not merely to achieve apredetermined clamping load on one set of fasteners, since this can bereadily done in the laboratory by instrumenting the bolt. The goal is toachieve consistent and reproducible clamping loads or final tensionvalues in large lots of fasteners at a low cost per fastener. Thus, themajor fallacy in prior art inferential tightening techniques has been toselect a fixed tightening parameter, such as torque or angle in thetorque control and turn-of-the-nut methods respectively, or a fixedrange of a particular tightening parameter and terminate tightening inresponse to the attainment of the fixed tightening parameter or rangethereof. This broad approach of the prior art has several majordifficulties. First, the critical item in tightening is clamping load asmay be measured by final bolt tension. With the possible exception ofsome of the acoustic methods, no one has apparently heretofore been ableto inferentially determine final bolt tension in production operations.Second, because of the selection of some parameter other than tension,there is introduced such widely variable factors as frictioncoefficients, speed related losses, and the like which grossly affectthe relationship between the fixed tightening parameter or the fixedrange thereof and the only important result in tightening, which isclamping load or bolt tension.

In one aspect, this invention contemplates the determination, duringtightening, of the value of a tightening parameter which is sufficientto tighten each fastener pair to a final desired tension value, whichparameter varies from one fastener pair to the next. Tightening of thefastener pair is then terminated in response to the variable value ofthe determined tightening parameter. By this approach, the variation infriction from one fastener pair to the next is largely eliminated. Thetechnique of this invention produces typical tension scatters on theorder of less than ±10% in production quantities whereas scatters withturn-of-the-nut techniques are at least 2-3 times higher and scatterwith torque control techniques are at least 5-6 times higher. It isaccordingly apparent that this invention produces substantially moreconsistent tightening results than do the significantly inaccuratetechniques of the prior art.

In another aspect, an important part of this invention consitutes thequality control procedures that are conducted as a consequence of theacquistion of torque and angle data of each fastener tightened. Most ofthe quality control procedures are done well prior to the termination oftightening and include procedures for determining whether the prevailingtorque of the fastener is too high, determining whether the torque rateof the fastener is linear or arcuate, determining whether the torquerate of the fastener is too low, determining whether the tool isperforming normally and determining whether the fastener has exhibitedsignificant non-linear strain. Any of the fastener related qualitycontrol checks are used to prematurely terminate tightening in the eventindications are that the fastener or its mating engagement with theclamped pieces is defective. The tool related quality control checksprovide a warning so that maintenance attention can be given to thetool.

It is accordingly an object of this invention to provide a technique fortightening threaded fasteners which produces substantially moreconsistent results than the prior art.

Another object of the invention is to provide a tightening techniquewhich provides sufficient data to conduct a number of quality controlprocedures during tightening.

Another object of this invention is to provide an improved technique fortightening threaded fasteners incorporating monitoring the torque-anglecurve, calculating the tension in the fastener being tightened andinstructing a tool to tighten the fasteners to a final desired tensionvalue.

Another object of this invention is to provide an improved technique fortightening threaded fasteners incorporating the monitoring of thetorque-angle relationship, calculating during tightening the tensionappearing in the fastener being tightened and instructing the wrench tocontinue tightening until a predetermined value of torque or angle isobtained which corresponds to the final desired tension value.

Other aspects, objects and advantages of this invention will becomeapparent as the description proceeds.

IN THE DRAWINGS

FIG. 1 is an illustration of typical torque-angle and tension-anglecurves generated during the continuous tightening of a fastener pair farbeyond the elastic limit;

FIG. 2 is an enlarged illustration of the low end of a typicaltorque-angle curve illustrating very early torque-angle relationship;

FIG. 3 is an enlarged illustration of a typical torque-angle curveconstituting a continuation of FIG. 2;

FIG. 4 is an illustration of a typical torque-speed relationship of anair powered tool;

FIG. 5 is a torque-angle diagram illustrating the determination ofnon-linear strain in the fastener at the mid-point stop;

FIG. 6 is an illustration of a typical tension-angle curve representingthe relaxation of a joint at the termination of continuous tightening;

FIG. 7 is an illustration of a typical tension-angle curve representingthe relaxation of the joint at the mid-point stop during tightening to ahigher tension value;

FIG. 8 is a torque-angle diagram illustrating the determination ofnon-linear strain in the fastener during tightening toward a finaltightening parameter;

FIG. 9 is an enlarged illustration of torque-angle and tension-anglecurves graphically explaining another facet of the invention;

FIG. 10 is a schematic view of the mechanism of this invention;

FIG. 11 is a side view of a component of the mechanism of FIG. 10;

FIGS. 12A and 12B are circuit diagrams of another component of thedevice of FIG. 10;

FIG. 13 is a front view of a typical operator's console;

FIG. 14 is a graph illustrating the relative effectiveness of thisinvention compared to prior art techniques; and

FIG. 15 is a block diagram illustrating another mechanism of thisinvention.

Referring to FIG. 1, there is illustrated a typical torque-angle curve10 and its corresponding tension-angle curve 12 which are developedduring the continuous threading of a fastener pair to a point far beyondthe elastic limit of the bolt, as may be measured in the laboratory bysuitable equipment. In the torque curve 10, there is typically a freerunning region or period 14 where only a small torque is required toadvance the nut and no appreciable bolt tension exists. This is followedby a region or period 16 of incipient clamp up where the joint parts arebeing brought toward engagement. This is followed by an engagementperiod or region 18 where the contact between the surfaces of thefastener and the clamped pieces are being established while the rate ofangle advance is gradually being reduced in accordance with thetorque-speed characteristics of the tool employed. The tension rate FR₁in the region 18 is typically less than the ultimate tension rate FR₂but is rather well defined. The engagement period 18 appears to cover anapproximate tension range of about ten percent to about fifty percent ofthe elastic limit of the bolt. Above the engagement region 18 is a finaltensioning region or period 20 which normally exhibits an increasedtension rate FR₂. Fortunately, FR₁, FR₂ and the location of the bendtherebetween are normally well defined and reproducible properties ofthe joint and are not related to friction or other variable factorswhich may develop in the course of tightening.

The torque rate is essentially zero in the free running region 14 andbegins to rise substantially during the incipient clamp up period 16.The torque rate TR in the engagement period 18 approaches linearity. Dueto the existance of speed-dependent losses such as lubricant squeezefilm and microplasticity of the surface irregularities between thefastener parts and clamped pieces, a linear approximation of the torquecurve 10 in the region 18 does not intersect the angle axis at the pointof origin of the tension curve 12. An offset angle α_(os) exists whichis proportional to such speed dependent losses. α_(os) describes theangular separation between the origin of the average torque slope TR andthe origin of the average tension slope FR₁. Because of the torque-speedcurve of the tool employed, it can be shown that α_(os) is torque ratedependent so that the offset torque T_(os) is the appropriate jointproperty and T_(os) is the product of the offset angle α_(os) and thetorque rate TR.

The elastic limit 22 occurs at a point beyond which strain is notrecoverable upon unloading and appears toward the upper end of the finaltightening region 20 as is well known in classical mechanics. Somewherein the yield region 24, the bolt commences to deform plastically ratherthan elastically. As alluded to previously, the normal definition of theyield point is in range of 0.1-0.2% strain which is somewhat arbitrary.The proportional limit occurs substantially below the yield point 22 andoccurs where the stress/strain ratio is no longer constant.

In order to implement the hereinafter disclosed method of tensioncontrol, one needs to determine FR₁, FR₂, T_(os) and other parameters asdiscussed more fully hereinafter. This conveniently accomplished byselecting a reasonably large sample of the fasteners that ultimatelywill be tightened by the technique of this invention and empiricallydetermining the values in the laboratory. It will normally beexperienced that scatters in FR₁ and either FR₂ or r, the ratio of FR₂/FR₁, will be quite small. In new bolts, FR₂ is normally 5-15% higherthan FR₁. In fasteners that have previously been tightened, FR₂ isnormally quite close to FR₁. The conclusion is that the differencebetween FR₁ and FR₂ is related to the microplasticity of surfaceirregularities between the mating faces of the joint. As is true is alltorque measurements, T_(os) will have much larger scatters. Fortunately,the offset torque correction is normally quite small so that its lack ofconsistency has a quite minimal effect of the final tension values. Oneexception is in the use of so-called "prevailing torque" fasteners whichusually comprise a bolt or nut having the threads intentionally deformedfor various reasons. Another exception involves the use of a bolt or nutin which the threads are unintentionally deformed. In such situations,the normal value of T_(os) should be increased by the addition of themeasured "free running" or prevailing torque or this effect compensatedfor as more fully explained hereinafter.

Broadly, the technique of this invention is to periodically orcontinuously sense the torque applied to the fastener pair and the angleof advance corresponding to the sensed torque, determine the tensionappearing at least at one joint 26, calculated a value of a tighteningparameter sufficient to achieve a final desired tension value F_(D) andinstruct a tool to advance the fastener pair until the attainment of thetightening parameter.

During a study of torque-tension-angle relationships, it was discoveredthat the inverse of the rate with respect to angle of the logarithm oftorque is theoretically a measure of bolt tension irrespective of jointfriction. Defining,

    P.tbd.d/dα log T                                     (2)

    F∝1/P, α>α.sub.q                        (3)

where αq is the angle where P achieves a maximum value and conceivablycould be used as the origin for the turn-of-the-nut method therebytotally eliminating the influence of joint friction. In practice, it isdifficult to detect a single meaningful peak which can be labeled α_(q)because of the noise inherent in the actual torque-angle signal.Although the concept expressed in equation (2) is valid, it requires adifferent procedure for processing the torque-angle data to achieve apractical solution. As will be apparent to those skilled in the art, thesolution may be analog or digital. The theoretical basis for equation(2) can be derived from equation (1). Differentiating equation (1)relative to angle, ##EQU1## Dividing equation (4) by equation (1),##EQU2## Since dT/T is the definition of d log T, ##EQU3## If dF/dα, thejoint tension rate, is a constant, then: ##EQU4##

Equation (7) shows that the constant of proportionality in equation (3)is the tension rate FR.

Several assumptions have been made in the above derivation:

(1) The tension rate is a constant. This is not precisely truethroughout the tightening range. The more precise assumption would havebeen that tension at any angle of advance after the angle of origin,where the tension rate commences, is a unique function of the joint andtherefore that the tension rate at any angle after the angle of originis a unique function of the joint.

(2) Torque is not a function of the turning speed. This is not strictlytrue and for accurate application, it should be accounted for.

(3) Joint friction (f_(h), f_(th)) is not load dependent for any onesample. This is a good assumption except when nonmetallic (molybdenumdisulfide, Teflon, etc.) coatings are utilized. Even in the case ofnon-metallic coatings, any changes in a finite tension range should besmall.

For purposes of convenience, the tightening technique of this inventionmay be referred to as the logarithmic rate method.

The importance of equations (5) and (7) should now be appreciated. Ithas been demonstrated in the laboratory that the value of tension ratedF/dα is a function of the joint having small scatter and is independentof friction. The torque rate dT/dα can be determined from torque andangle measurements taken during the tightening of each fastener pair bysuitable torque and angle sensors on the tightening tool. The torquevalue T is, of course, measured by same torque transducer. It willaccordingly be apparent that the friction dependent parameters, i.e.torque rate and torque, are determined for each fastener duringtightening, which is here defined as the time frame commencing with theonset of threading and stopping at the termination of tightening. Sincetension rate dF/dα is a function of the joint which is determinedempirically prior to the tightening of production fasteners, it is asimple matter to solve equation (5) for tension.

While theoretically correct, several adjustments should be made toequations (5) or (7) in order to enhance accuracy and reliability.First, the effect of prevailing torque T_(pv) should be taken intoaccount. Prevailing torque is that torque necessary to overcome thethread-to-thread resistance to fastener advance which does notcontribute to the inducement of bolt tension and which may be sensedduring the threading advance of the fasteners in the region 14. Second,the effect of offset torque T_(os) shoud likewise be taken into account.Offset torque is that torque necessary, at zero prevailing torque, toadvance the fastener to an angle location corresponding to the origin oftension. These accomodations may be expressed mathematically as:##EQU5##

The importance of equations (8) and (9) should now be appreciated.

Referring to FIG. 1, it may be assumed that the fasteners are threadedtogether with measurements being taken of both torque and angle withtightening being advanced to the point 26. The average torque rate TR iscalculated, as by the use of the least squares method. Since the tensionrate FR₁ is known from empirical measurements of the joint in question,the tension in the joint can be calculated at the point 26 from equation(5) or (9). Graphically, the angle required to advance the fastenersfrom the tension value calculated at the point 26 to the final desiredtension value F_(D) can be easily done since the tension rate FR₂ haslikewise been determined empirically. After determining the additionalangle α_(final), the tool may be instructed to so advance the fastenersthereby attaining the desired final tension value F_(D). In a similarfashion, the additional torque ΔT or the final desired torque T_(D) canbe calculated.

There are substantial difficulties in applying these principles toproduction line operations. It will be apparent that the calculationsbeing made are being done while tightening. It will be apparent that theduration of tightening should be minimized so far as practicablecommensurate with the attainment of consistent results. In any event, itwill be apparent that long tightening times, for example two minutes,would render the technique unsuitable for many production lineoperations although some suitability may remain for special purposeapplications such as in the fabrication of reactor vessels, aircraft andthe like where precision is paramount. It is accordingly evident thatthe use of electronic computation techniques is highly desirable forprocessing the data obtained from measurements taken during tightening.Even with the use of electronic computation techniques, it is desirableto advance the fasteners for some initial distance, suspend tighteningmomentarily and then resume tightening to the final desired tensionvalue. The momentary stop allows time to complete lengthly calculationsand has the additional benefit of allowing the joint to relax at thispoint rather than at the final tension value attained. As will be morefully apparent hereinafter, many of the calculations are being donewhile the tool is running as well as when the tool is momentarilystopped. It will, however, be evident that simplified computations maybe utilized thereby eliminating the necessity for a momentary pause inthe tightening operation.

More specifically, the following steps may be taken to attain aconsistent bolt tension utilizing an instructable tool equipped tomeasure torque and angle information only, after the acquisition ofcertain empirical information:

1. Engage the fasteners, start the tool and record torque atpredetermined angle increments.

2. Shut the tool off in a tension range of 0.4-0.75 of elastic limit.Although a turn-of-the-nut approach or torque control strategy may beused to estimate the initial tool shut off, a simplified logarithmicrate method in accordance with this invention provides more consistentresults.

3. Calculate the torque rate from the torque and angle measurements by asuitable smoothing technique, e.g. least squares. Calculate the torqueat the mid-point of the range from which the torque rate was calculated,by averaging the torque value along this range. The intersection of theaverage torque rate with the axis represented by (T_(pv) +T_(os)) isaccordingly established. Since the offset torque T_(os) is largely afunction of the joint, the intersection of the tension curve with theangle axis is established.

4. The tension curve is then a straight line emerging from the origin orintersection determined in (3) above with the initial slope FR₁. This istypically valid up to about 0.5 elastic limit at which point the tensioncurve has a slope of FR₂. The location of the bend in the tension-anglecurve is determined empirically when determining the values of FR₁, FR₂and T_(os).

5. Calculate the tension value appearing in the fasteners at somelocation, for example, point 26. Given the tension value at point 26,calculate the additional angle α_(final) or the additional torque ΔTnecessary to tighten the fasteners to the final desired tension valueF_(D).

6. Instruct the tool to resume tightening and advance the fastenersthrough the angle α_(final) or for the increased torque ΔT.

As disclosed in applicant's copending application Ser. No. 766,429, nowU.S. Pat. No. 4,106,570, the disclosure of which is incorporated hereinby reference, the angle of advance measured by an angle encoder is notthe true angle through which the fastener turns because of torsionaltwist in the tightening tool and because of torsional twist in the bolt.To achieve maximum accuracy, it is necessary to compensate the measuredangle of advance for the torsional twist of the tool and bolt. Inaddition, it is necessary to take into account the torsional twist ofthe laboratory equipment utilized to acquire values for the tensionrates FR₁ and FR₂.

For purposes of discussion, the implementation of the technique of thisinvention may be broken down into six generally chronological segments:(1) quality control procedures in the regions 14, 16; (2) reaching themid-point stop and conducting torque rate determinations and qualitycontrol procedures; (3) procedures determining the final shut offparameters; (4) procedures involving restarting the tool; (5) proceduresdetermining the occurrence of non-linear strain during tightening towardthe final shut off point; and (6) quality control procedures conductedat the termination of tightening.

QUALITY CONTROL PROCEDURES IN THE REGIONS 14, 16

It has been learned that considerable information can be acquired aboutthe quality of the fasteners during the free running region 14.Specifically, deductions can be made about cross threading, grosslyimperfect threads, bolt bottoming, and whether the bolt is alreadytight. Because the joint has not clamped up, it is evident that theinformation so acquired concerns the fasteners only and is not affectedby other joint properties. It has also been learned that deductions canbe made during the incipient clamp up region 16 concerning the tool.Specifically it can be determined whether the tool has engaged thefastener, whether a fastener is in place, the bolt is broken, one of thethreaded members has no threads, or one of the threaded fasteners is thewrong size.

Prevailing Torque

Although the region 14 is referred to as the "free running" region, asmall amount of torque is necessary to advance the fasteners because offriction between the mating threads. Some types of fasteners, known asprevailing torque fasteners, include intentionally imperfect threadswhich require more than a minimum amount of torque in order tothreadably advance. Other fasteners which are unintentionally imperfectalso require more than a minimum torque to effect threadable advance.For all practical purposes these types of fasteners may be treatedidentically with one caveat. Any batch of fasteners which are notintended to be prevailing torque fasteners will include some fastenerswhich have substantially perfect threads thereby requiring only aminimum torque and will also include some fasteners having imperfectthreads which require more than a minimum torque for threadable advance.Thus, any technique which is intended to be universal or which isintended to be used with non-prevailing torque fasteners must have thecapability of accomodating fasteners which vary from substantiallyperfect to grossly imperfect.

Broadly, one goal of this procedure is to detect, during tightening inthe free running region 14, those fasteners which exhibit instantaneousprevailing torque values T_(pvi) which exceed a maximum expectedprevailing torque (T_(pv))_(max). The value of (T_(pv))_(max) may beacquired in any suitable manner, as by relying on the publishedinformation of fastener manufacturers, by measuring the prevailingtorque on a significant number of fasteners, or by adding an incrementalpercentage, for example 10-20%, to either published information oracquired values. Similarly, it may be desired to detect those fastenerswhich exhibit instantaneous prevailing torque values T_(pvi) which areless than a minimum prevailing torque (T_(pv))_(min), as when usingprevailing torque fasteners and assurance is required that the fastenersare up to specifications.

Another goal of this procedure is to acquire sufficient information toprovide a reasonably accurate value for average prevailing torqueT_(pv). This may prove to be of value in correcting a final shut offparameter for the effect of prevailing torque.

Several precautions are desirably taken for the measuring of prevailingtorque to assure that the data is reliable. First, it is essential thatthe acquisition of data occur before the commencement of clamp up of thejoint parts. Otherwise, the normal torque required to begin tighteningup the joint will be confused or erroneously deduced as abnormalprevailing torque. This error in data acquisition is fatal to properresults because applied torque rapidly increases during joint clamp upas is evident from the showing in region 16 of FIG. 1. Second, theacquisition of data should be delayed until the fastener parts arerotating or other steps should be taken to avoid spurious torquereadings from the static friction exhibited between the fastener partsat rest or due to the transition from static to dynamic frictioneffects.

With the criteria outlined above, it is evident that there isconsiderable leeway in designing a system for acquiring prevailingtorque data for a particular application. Because the need in aparticular application may be to reject defective parts, to acquirevalues for average prevailing torque T_(pv), or both, the designselections are subject to change.

In the system disclosed, utilizing the fasteners described immediatelypreceding Table II, it is desired to take prevailing torque data toreject fasteners at an early stage of tightening and to acquire anaverage prevailing torque value T_(pv) to compensate the final shut offparameter. Referring to FIG. 2, there is illustrated a typicaltorque-angle plot 28 of an acceptable fastener exhibiting an initialtorque peak 30 caused by static friction between the fastener componentsand the change over from static to dynamic friction. After the initialtorque peak 30, the curve 28 levels out to a reasonably constant valuebetween a minimum expected prevailing torque (T_(pv))_(min) and amaximum expected prevailing torque (T_(pv))_(max). Although the curve 28is illustrated as a continuously recorded value, in digital systems itis highly desirable to take torque sensings only at selected locationsspaced apart by a predetermined angle increment Δθ.

In operation, the tool is turned on to commence rotation of the fastenercomponent and a delay of one Δθ angle increment is allowed before afirst torque sensing 12 is taken. Thereafter, a torque sensing is takenat every angle increment Δθ, indicated by the data points 34, until theexpected rundown angle θ_(rd) is reached. During the expected rundownangle θ_(rd), the instantaneous torque sensing T_(pvi) at each of thedata points 32, 34 is compared with (T_(pv))_(max). If the instantaneousprevailing torque T_(pvi) exceeds (T_(pv))_(max) more than once, a shutoff command to the tool is issued, an indication is made that the jointis unacceptable and the system is reset for the next tightening cycle.Although it is normally desirable to have the tool operator intervenefollowing the rejection of a joint and although the typical air poweredtools used to tighten fasteners are not reversible, it may be desired insome applications to automatically back off the nut by providing areversible tool and instructing the tool to back the nut off prior toreset for the next tightening cycle. In connection with the fastenersexhibiting the curve 28, it is apparent that no shut off command isissued.

With the system designed in this manner, decisions need to be made aboutthe size of the angle increments Δθ, the size of the rundown angleθ_(rd), and the size of a sampling region θ_(s). The value of Δθ isselected so that the transient effect of the static-to-dynamic peak 30and any other transient effect will be sensed only once if at all. Ithas been found that the transient torque effects in the free runningregion 14 are of quite short angular duration. Although the value of Δθis susceptible to considerable compromise, a selection of 22° has provedsatisfactory. The value of the rundown angle θ_(rd) is selected toassure that both the rundown angle θ_(rd) and the period of dataacquisition θ_(s) immediately following θ_(rd) are completedsubstantially before the incipient clamps up region 16 commences. Thevalue of θ_(rd) accordingly depends on the duration of the samplingperiod θ_(s), the length of the threaded fastener compared to the sizeof the parts to be clamped up and the like. The selection of θ_(rd) andθ_(s) should be conservative to provide assurance that these angularperiods are completed prior to the incipient clamp up region 16. Thevalue of θ_(rd) may thus vary widely and in one embodiment of theinvention is five complete revolutions of the fastener or torque applingtool.

Similarly, the duration of the sampling region θ_(s) may also varywidely. It is not essential to take an enormous number of torquereadings to establish a reasonably reliable value for average prevailingtorque T_(pv) for the following reasons. It will be shortly apparentthat the value of T_(pv) is relatively small when compared to the torquereadings T from which T_(pv) will be subtracted. Accordingly, anydifference between the true average prevailing torque and the calculatedvalue will be smaller still. It is accordingly quite satisfactory toobtain an average value from a fairly modest number of data points, e.g.5-30. Although the duration of the sampling period θ_(s) is susceptibleto considerable compromise, a sampling duration on the order of onerevolution has proved satisfactory. Since prevailing torque T_(pv) iscreated by circumferential asymmetry of the nut and bolt, a selection ofone revolution for the sampling region θ_(s) is a natural one. Thesampling interval between the data points 36 in the region θ_(s) mayconveniently continue to be 22°. Accordingly, approximately sixteen datapoints 36 are used.

In calculating the average prevailing torque T_(pv) in the samplingregion θ_(s), there are a number of conceivable approaches. First, onemay merely add the values of the torque sensing T_(pvi) and divide bythe number of data points. In the alternative, one may elect to use asmoothing technique such as least squares. Furthermore, one couldconceivably average the torque sensings after disregarding any valueabove (T_(pv))_(max) and either arithematically averaging or smoothingthe remaining data. For reasons mentiond previously, any reasonablyaccurate averaging technique will suffice because the difference betweenthe calculated average and the true average will be a very small value.

It will be seen that by delaying the first data point 32 by the angleincrement Δθ from the onset of rotation, the existence of thestatic-to-dynamic peak 30 will likely be masked. By separating the datapoints 32, 34, 36 by the angle increment Δθ, any transient torque effectwill be sensed only once if at all. By delaying the sampling periodθ_(s) until after the rundown angle θ_(rd), one is reasonably assuredthat sampling for averaging purposes avoids any spurious sensingsrelated to the onset of tightening.

As will be more fully pointed out hereinafter, a reasonably reliablevalue for T_(pv) is desirable to compensate a final shut off parameterfor the effect of prevailing torque. In this regard, it will be evidentthat the amount of torque applied to a fastener during the free runningregion 14 has nothing whatsoever to do with the attainment of tension inthe bolt at the termination of tightening. The compensation made for thetightening strategy of this invention will be discussed more fullyhereinafter. In a torque control strategy, however, the running torquesensed by the torque encoder in the final tightening region 18 should beadjusted by the amount of the noted prevailing torque to obtain a torquevalue which can be compared to the desired torque shut off parameter.For example, if empirical data suggests that the fastener needs toadvance 30 ft-lbs above an average prevailing torque of 3 ft-lbs and thefastener being tightened exhibits a prevailing torque of 5 ft-lbs, thetool should be instructed either: (1) to advance the fastener to 35ft-lbs, or (2) to advance the fastener 30 ft-lbs beyond the notedprevailing torque of 5 ft-lbs, or (3) to advance the fastener until thedifference between the sensed torque and the noted prevailing torqueequals 30 ft-lbs. In a turn-of-nut strategy, the torque sensings used inreaching the angle location known as snug torque should be similarlyadjusted by the amount of the noted prevailing torque.

Also shown in FIG. 2 is a torque-angle curve 38 which clearly indicatesan undesirable fastener pair. The curve 38 exhbits a torque peak 40caused by the change over from static to dynamic friction and thenlevels out to a running value above (T_(pv))_(max). A preferredtechnique for determining when a fastener pair is unacceptable is theoccurrence of two torque sensings T_(pvi) above (T_(pv))_(max). Thetorque sensing at the first data point 32 is above (T_(pv))_(max) sothat when the second data point 34 is likewise above this value, thetool shuts off, the joint is indicated as being unacceptable and thesystem is reset for the commencement of a new tightening cycle.

It is evident that any system which rejects fasteners having excessiveprevailing torque sensings will reject the fastener pair exhibiting thecurve 38 and will pass the fastener pair exhibiting the curve 28. Thereare, however, a number of fasteners which exhibit a torque-angle curve42 which is distinctly different than either of the curves 28, 38. Thecurve 42 includes a static-to-dynamic peak 44 and then levels outinitially to a value below (T_(pv))_(max). The curve 42 also exhibits atransient peak 46 which is above (T_(pv))_(max) which is detected at thesubsequent data point 34. Thereafter, the curve 42 levels out below(T_(pv))_(max). It is highly desirable not to reject the fastenersexhibiting the curve 42 because the transient torque peak 46 does notrepeat or is not sensed more than once. Accordingly, the conclusion isthat the transient peak 46 is not indicative of a serious threadimperfection.

A somewhat different situation is evidenced by a torque-angle curve 48which exhibits a static-to-dynamic peak 50 and at least a pair ofsubsequent transient torque peaks 52, 54. In this situation, there areat least two instances where data taken at the points 34 indicate thatthe instantaneous prevailing torque T_(pvi) exceeds (T_(pv))_(max).Although it is within the bounds of judgment to accept fastenersexhibiting several transient peaks, such as illustrated by the curve 48,it is preferred to reject these fasteners.

It will accordingly be seen that there is provided a technique forrejecting threaded fasteners at an early stage of the tightening cyclein response to a torque sensing indicative of serious fastenerimperfections.

If fasteners are often rejected because of high T_(pvi) sensings, it maybe concluded that the batch of fasteners is suspect. Accordingly, arunning average of rejections to fasteners run is conducted. If

    R.sub.pv /N≧E                                       (10)

where R_(pv) is the number of fasteners rejected, N is the sample sizeand E is a fractional value acceptable to the user, such as 0.15, asignal is displayed at the operator's station to indicate a partsdefect. The value of N is preferably not the cumulative number of jointstightened but is a running value, as by storing, on a first-in,first-out basis, a finite number of joints tightened, such as 30.

In the event that prevailing torque fasteners are being tightened and itis desired to determine that the fasteners do exhibit prevailing torque,it appears that the check to be made is to compare average prevailingtorque T_(pv) with (T_(pv))_(min). In the event that T_(pv) is less than(T_(pv))_(min), the fasteners should be rejected.

Is Tool Advancing Fastener?

Another quality control procedure conducted early in the tighteningcycle is to determine whether the fastener is threadably advancing. Thisis accomplished by measuring the time elapsed between the instant thetool is turned on until the torque encoder senses a predeterminedminimum torque T_(sth) which is the threshold torque stored by the dataprocessor after the preliminary data points 32, 34, 36. To establishT_(sth), a torque value T₁ is empirically determined and is the firsttorque value utilized to calculate a preliminary torque rate asdiscussed hereinafter. T₁ is on the order of about 20-30% of the averagefinal torque value obtained in running the same to empirically determineFR₁, FR₂ and T_(os). When the storing threshold torque T_(sth) is sensedto be

    T.sub.sth =0.25(T.sub.1 +T.sub.pv)                         (11)

the data processor begins to store torque values sensed by the torqueencoder. If the data processor does not commence to store torque valueswithin a very short period, on the order of 3-10 seconds, of the onsetof tool turn-on, the conclusion is that no bolt is present, the toolsocket has not engaged the bolt head, the bolt is broken, one of thethreaded members has no threads, or one or the threaded members is thewrong size. In this event, a signal is generated by the data processorto turn off the tool, signal that one of these conditions exists andreset the tool for the next tightening cycle.

REACHING THE MID-POINT STOP, TORQUE RATE PROCEDURES, AND QUALITY CONTROLPROCEDURES Reaching the Midpoint

The intent at the mid-point stop is for the joint to be tightened to anangular location corresponding to the break in the tension-angle curvefor reasons more fully pointed out hereinafter. Although a torquecontrol or turn-of-the-nut method can be used to determine the mid-pointstop, it is preferred to use a simplied logarithmic rate method inaccordance with this invention. Referring to FIG. 3, which is acontinuation of the normal torque-angle curve 28 of FIG. 2, the toolcontinues to turn the fasteners with torque values being recorded andstored at fairly small equal angle increments which may be, for example,in the range of 0.2°-3°.

The angle encoder may conveniently be of the digital type to deliver apulse at small, equal angle increments. The unit of angle used forcalculation purposes is Δα which is one or more multiples of the anglepulse. The value for Δα depends on the elastic properties of the jointand typically are in the range of 0.5°-6° although a wider range isacceptable in some circumstances. With fasteners of the type studied, aselection in the range of 2°-3° seems preferable. In getting to themid-point, torque and angle measurements obtained in the region 16 areused.

Referring to FIG. 3, when running torque is first sensed to be equal toor greater than T₁, such as at the location 56, the angular position ofthe location 56 is noted and stored. When the tool passes the point 58which is one α_(k) degrees beyond the location 56, the torque value T₂is sensed and stored. The value of α_(k) is preferably large enough togive a rough approximation for a preliminary torque rate, which iscalculated as (T₂ -T₁)/α_(k). If α_(k) were very large, the tool wouldnot be stopped until late, leaving little or no additional room toresume tightening. If α_(k) were very small, the value of torque ratecalculated from (T₂ -T₁)/α_(k) would be so influenced by noise in thetorque sensings that it would be unreliable. The actual value of α_(k)depends on the elastic properties of the joint. A compromise of 9° forα_(k) has proved acceptable for the particular joint describedpreceeding Table II although other compromises are obviously acceptable.

The data processor then calculates α₁, in accordance with the followingequations: ##EQU6## α_(d) is the desired angle from tension origin tomid-point and is F_(M) /FR₁ or slightly greater where F_(M) is thetension value at the junction of the two tension regions indicated byFR₁ and FR₂, α_(or) is the tool overrun at idle due to actuation delay,T_(o) is the stall torque of the tool, K_(o) is a typical torque ratefor the particular fasteners involved and is determined empirically, andN₁ and N₂ are correction factors necessitated by the inaccuratealgebraic expansion of more precise equations, which expansionsubstantially reduces calculation time compared to the exact equations.It will be apparent that, in a production line situation involving thesame size bolts and the same size tools, every value in these equations,except T₂ and T_(pv) can be reduced to numbers before starting. Thus,the computations are actually easier and quicker than appears.

It might be questioned why the value of α_(k) is of any importance sinceneither equation (12), (13) or (14) appears to contain a value forpreliminary torque rate. Equations (12), (13) and (14) constitute oneapplication of the logarithmic rate method to achieve a mid-pointtension value of FR₁ α_(d) with provisions made for tool overrun duesolely to the time delay between the shut off command and exhaustion ofair from the tool. The mathematical complexities have, by design, beentransferred from equation (12) to equations (13) and (14) so thatcomputation of equation (12) during tightening requires the leastpossible elapsed time. Equations (13) and (14) can be computed manuallyeither prior to system installation or computed by the microprocessorwhen in a dormant portion of the tightening cycle, for example, prior tothe initiation of tightening. Although the preliminary torque rate (T₂-T₁)/α_(k) does not appear in equations (12), (13) or (14) as written,if one were to substitute the equations for a and c into equation (12),one would find that the preliminary torque rate appears. Accordingly,the reasons why α_(k) should not be too large or too small are aspreviously discussed.

As will be recognized by those skilled in the art, equations (13) and(14) do not include a tool overrun prediction due solely to the inertiaof the rotating parts of the tool. For moderate and high torque ratebolts, the amount of angular overrun due solely to inertia is ratherinsignificant. The reason, of course, is that the tool is not rotatingvery fast. With low torque rate bolts, which the tool is able to turnfaster, the amount of overrun due solely to inertia is still modest. Forapplications where maximum accuracy is desirable, equations (13) and/or(14) may be modifed to incorporate a measure of overrun prediction basedon inertia.

The determination of the mid-point stop is of some importance as may bevisualized from an appreciation of FIG. 1. It will be recollected thatit is desired to calculate the average torque rate TR. If the mid-pointstop occurs, for example, in the lower part of the region 18, theaverage torque rate will be substantially too low. If the mid-point stopis too late and well into the region 20, two difficulties are presented:(1) the calculated torque rate TR may be substantially too high althoughsome calculations can be done to disregard some of the later data inorder to shift the range where torque rate calculations are actuallybeing conducted, and (2) there may be little or no additional roomavailable to resume tightening to the final desired tension valueconsidering allowance for tool overrun.

Referring to FIG. 3, the tool is commanded to shut off at a point 60which is α₁ degrees beyond point 56 which was where the torque value T₁was first equalled or exceeded. Because of the time delay in the toolfrom the shut off command until the tool actually stops, which isrepresented by the point 62, the tool has overrun by an angle δα. Themid-point stop 62 typically falls in the range of about 0.4-0.75 of theelastic limit. For any given application, the empirically determinedvalues act to establish the mid-point stop 62 at a given fraction of theelastic limit which is not changed until new empirical data is developedwhich, as for example, may occur when a different type fastener isselected.

Torque Rate Procedures

In order to calculate the average torque rate TR, a decision must bemade of which torque and angle measurements are to be used. It has beenlearned that the torque sensings approaching the stopping point 62 aresomewhat unreliable because of speed dependent variables. Accordingly,in the computations conducted to determine average torque rate TR, thosesensings which are affected by the act of stopping are disregarded.Although more than one torque sensing may be discarded in order toprovide greater assurance, it is assumed for purposes of simplicity thatonly the last torque value is ignored. Accordingly, the highest torquevalue used in the torque rate calculations is at a location 64 which isone Δα backward from the point 62. The torque value at the point 64 isT₃. The total number of values used in torque rate calculations,designated n for more general purposes, may vary widely and is subjectto considerable compromise. A total of fourteen consecutive data pointshas proved quite acceptable. The mean torque T_(m) and the averagetorque rate TR are then calculated using the following summations wherei is a designation for each point selected for the torque ratecalculations and T_(i) is the torque value there sensed: ##EQU7##Equation (15) will be recognized as merely adding the torque valuesoccuring at each of the points i and dividing this sum by the totalnumber of data points n. Equation (16) will be recognized as a leastsquares fit for the data points i.

It is desirable to assure that the mean torque T_(m) and the averagetorque rate TR are taken over substantially the same tension rangeduring the tightening of each fastener pair. This may be accomplished bychecking to determine how close the angular position of the stoppingpoint 62 is to the break in the tension-angle curve 12. The angularposition of the mean torque T_(m) along an abcissa T_(os) +T_(pv) may becalculated from the equation: ##EQU8## The angular distance from thepoint of origin of the tension curve 12 to the stopping point 62 may becalculated from actual data derived from the fastener being tightenedfrom the equation:

    α.sub.origin =-1/2(n+1) Δα-α.sub.F where α.sub.origin =0.                                    (18)

For calculation purposes, it is desirable that α_(origin) be a negativevalue. From empirically determined information done prior to thetightening of production fasteners, the start of the second tensionregion may be calculated from the equation: ##EQU9## where F_(M) is thetension value at the break. The difference between α_(origin) andα_(F).sbsb.M may be obtained from the equation:

    X=-α.sub.origin -α.sub.F.sbsb.M.               (20)

It will be remembered that α_(origin) is a negative value.

If X≧0, this means that the mid-point stop 62 is too late andconsequently that the largest torque value T₃ in the torque ratecalculations is too large. Without revising the value for TR, TR willtend to be too high as previously discussed. Accordingly, one needs toshift the range of torque rate calculations downwardly on thetorque-angle curve illustrated in FIG. 3. Thus,

    n.sub.H =↓(X/Δα)+1; and                 (21)

    n.sub.1 =n.                                                (22)

From the stopping point 62, one moves downwardly along the torque-anglecurve by n_(H) angle increments of Δα to define a new point 66 as theupper limit of the range through which torque rate will be calculated.The symbol ↓ means that any fractional value is dropped so that thenumber used is the next lowest integer from the calculated value. Thetotal number of data points n remains the same.

If X≦0, this means that the stopping point 62 occured too soon whichwould tend to give a value for torque rate that is too low. Since onecannot move upwardly on the torque-angle curve to obtain an additionalarea of measurement, the practical solution is to accept fewer datapoints for torque rate calculations thereby, in effect, lopping off thelower end of the range. Accordingly, ##EQU10## where n_(H1) indicatesthat the point or location where the largest torque value used in thetorque rate calculations occurs. Since the largest torque value willremain the same, n_(H1) =1 so that the torque T₃, being Δα removed fromthe stopping point 62, is the largest torque value used. The new valuefor n₁, which is the total number of data points used, is based on theassumption that the tension rate in the first region is substantiallylinear above a minimum tension value F_(L), determined empirically, andthat the tension F_(o) in the joint at the stopping point 62 lies in thefirst tension range. The symbol ΔF is the additional tension in thefirst tension range per angle increment Δα and may be expressedmathematically as:

    ΔF=FR.sub.1 Δα                           (25)

The tension F_(o) in the joint at the stopping point 62 is

    F.sub.o =-FR.sub.1 α.sub.origin where X≦0, or (26)

    F.sub.o =F.sub.M +rFR.sub.1 X where X>0                    (27)

where F_(M) is the empirically determined tension value at the break inthe tension curve 12 and r is the ratio of FR₂ /FR₁.

It is conceivable that n₁ may be too small, e.g. two or three points, togive good results with the least squares equation (16). Accordingly, acheck is made to determine if n₁ is less than one half of n. In thisevent, ##EQU11## and n₂ is used as the total number of data points.

Accordingly, a new summation is performed for mean torque T_(m) andtorque rate TR in accordance with equations (15) and (16) utilizing thenew starting place in the event that X≧0 or starting with the samehighest torque value but using fewer number of data points in the eventthat X<0.

With revised values for mean torque T_(m) and torque rate TR, a revisedvalue may be obtained for the angle of origin of the torque-angle curveusing equation (17) and a revised value and for the origin of thetension-angle curve using equation (18). A calculation is again made todetermine whether the tool has overshot or undershot the break in thetension curve in accordance with equations (19) and (20). Calculationsare again made for the tension value F_(o) at the stopping point 62. Itwill be apparent that the values of mean torque T_(m), torque rate TR,α_(F), α_(origin), F_(o) and the like may be revised as many times asdesirable. It is also conceivable not to conduct the second pass undersome circumstances.

Quality Control Procedures--Torque Rate Curvature

One of the defects in the technique heretofore described is theassumption that the empirically determined tension rate FR₁ correctlydescribes the elastic properties of the joint actually being tightened.For good quality joints, the tension rate FR₁ does not vary widely.There are, however, a number of relatively common situations, e.g.galled threads, misaligned fasteners, poor contact surfaces, dirt orother foreign particles between the contact surfaces, and the like,where the actual tension rate for the joint being tightened issinificantly below the empirically determined tension rate FR₁. In suchpoor quality joints, the actual final tension value will besignificantly below the desired tension value F_(D) and significantlybelow the final calculated tension value F_(final). To determine thesignificance of such poor quality joints, two 5/16"-24, SAE grade 8 nutsand bolts were tightened with a shim, 0.015 inches in thickness,inserted from one end under the bolt in order to simulate poor contactdue to misalignment. The final desired tension value F_(D) was 5500pounds. The actual measured final tension value was 2400 pounds and 1700pounds for the two fasteners, a percentage variation of -56% and -69%from desired. It will accordingly be apparent that the occurrence ofsuch poor quality joints can have a major effect on the scatter seen infasteners tightened by the technique of this invention. It will also beevident, upon reflection, that such poor quality joints will have a likeeffect on the scatter in fasteners tightened by a turn-of-the-nutmethod.

It has been learned that poor quality joints of the type exhibitingabnormally low tension rates can readily be detected by the data encodedand stored during the course of tightening a fastener pair with thisinvention. In such poor quality joints, the torque rate is not constantin the upper part of the region 18 where the average torque rate TR iscalculated, as contrasted to the showing of FIG. 3. Instead, thetorque-angle plot is arcuate and, if plotted, is upwardly concave. Thus,it is a relatively simple manner to measure or calculate and thendirectly compare the average torque rates in the upper and lower partsof the range where the torque rate TR is calculated. For example, in asituation where thirteen data points are being used to calculate TR,with the point 64 being the highest torque value used, the torque rateTR_(a) over an angle of six Δα increments backward from the point 64would be calculated. The calculations may, of course, be a two point ora least squares technique. Next, the torque rate TR_(b) over an anglecommencing with six Δα increments backward from the point 64 and endingtwelve increments backward from the point 64 is calculated by a twopoint or least squares technique. Then, the ratio of TR_(a) /TR_(b) iscomputed. If the ratio of TR_(a) /TR_(b) is near unity, e.g. 1±0.10, theconclusion is that the joint has an acceptable tension rate. If theratio of TR_(a) /TR_(b) diverges significantly from unity, e.g. TR_(a)/TR_(b) >1.10, the conclusion is that the joint has an abnormally lowtension rate FR₁ and, if tightened by the technique of this invention orby a turn-of-the-nut method, will result in a fastener stressedsubstantially below the desired tension value F_(D). A suitable signalmay be displayed at the operator's station, the joint rejected and theparts replaced.

Rather than directly checking the curvature of the torque-angle plot,indirect methods are available. One approach is to compare the values ofthe calculated mid-point tension F_(o) in the first pass with that inthe second pass. This is, in effect, calculating a first tension valueat a predetermined location using a torque rate in a first area,calculating a second tension value at the same location using a torquerate in a second area and then comparing the first and second tensionvalues. If the two values deviate by more than about 13%, joint problemsare highly likely. The figure 13% is, of course, somewhat arbitrary. Itis based on the expectation of tension control of ±10% within threestandard deviations, a mean shift of 2% plus 1% for other uncertainties.The selection of 13% rarely produces false signals when parts havereasonable quality. If a better number is available, it should be used.

Quality Control--Torque Rate Too Low

As will be appreciated, the torque rate calculations are conducted oneach successive fastener in the same tension range, i.e. F_(L) -F_(H),the values of which are determined empirically. If the torque rate TR isunsually high, the conclusion is that the fastener pair exhibits veryhigh friction. In the practice of this invention, there is nothing wrongwith high friction rates and consequently no upper limit on the torquerate TR is specified. Unusually low values of TR are, however, cause forconcern. First, the theoretical minimum torque rate TR° is not zerobecause the tool does reversible work on the joint in the absence offriction by producing tensile stress in the bolt and compressive stressin the clamped pieces and nut. When friction is zero, it can be shownthat

    TR°=(w/2π)FR>0                                   (29)

where TR° is the theoretical minimum torque rate and w is the pitch ofthe threads. Accordingly, TR° is positive and its value depends onthread pitch and the joint tension rate. The observed torque rate TR ismade up of TR° and TR_(f) which is the friction component. If it isassumed that friction can change at most ±60% from its expected value,represented by the typical torque rate TR_(o), then the minimum expectedtorque rate TR_(min) under normal conditions can be expressed by:

    TR.sub.min =0.6TR°+(1-0.6)TR.sub.o.                 (30)

The factor 0.6, representing a 60% change in friction coefficient, issomewhat arbitrary. If a better estimate is available, it should beused. Whenever a torque rate less than TR_(min) is observed, itindicates a joint problem. This could mean wrong parts, poor contactbetween the parts, or poor data processing, e.g. if the mid-pointtension F_(o) is far too low. In any event, when the calculated torquerate TR is less than TR_(min), a signal is given to indicate that thejoint is rejected. Because this calculation is conducted during themid-point pause, the tool is already off. Accordingly, the tool is resetfor a new tightening cycle. It will be appreciated that this approach isa direct technique for assuring that TR exceeds TR_(min) for acceptablejoints.

There are, however, techniques for indirectly detecting very low torquerates. A first indirect technique involves the second pass or secondcalculations for TR. The second pass requires a value of n_(H) greaterthan one. When TR is abnormally low, the first estimate of F_(o) is verylarge leading to a value of n_(H) so great that the location of F_(L)lies outside the stored data, i.e. F_(L) appears to lie below the torquestoring threshold T_(sth). Another indirect approach is to compare thecalculated tension F_(o) at the mid-point with the final desired tensionF_(D). If they are too close, the observed torque rate TR must beunusually low.

Quality Control--Tool Performance

One of the advantages of the mid-point stop is that one obtains ameasurement of the actual amount of tool overrun δα occuring between theangular locations 60, 62 corresponding to the torque values T₄ andT_(d). This allows for a check of tool performance. Although the tooloverrun at the termination of tightening may be used to determine toolmalfunction, this operation is more conveniently and accuratelymonitored during overrun adjacent the mid-point stop 62.

When the tool is instructed to stop, it takes some time for all motionto cease. For any given tool speed at the time of the shut off command,there exists a given angle of rotation that occurs before all motionceases. There are two phenomena that affect tool overrun: (1) the timelapse between the issuance of the shut off command and the completeclosing of the air control value, and (2) the rotational inertia of therelevant pairs. By selecting appropriately designed rotors, the overrundue to inertia is noticeable only when idling. For purposes ofsimplicity, tool overrun due to inertia may be neglected.

There are accordingly two assumptions in tool overrun calculations: (1)overrun is due solely to time delay and the motor stops immediatelyafter the pair supply valve is completely shut off; and (2) the tool hasa linear torque-speed curve as shown in FIG. 4 which can becharacterized by two parameters, the stall torque T_(o) and the idleangular speed ω_(o) such that:

    T/T.sub.o =1-ω/ω.sub.o                         (31)

where T is the sensed torque at any location and ω is the angular speedat that location. On this basis, it can be shown that: ##EQU12## withonly a small error where δα_(a) is the anticipated angular overrun atthe time the applied torque is T_(a), α_(or) is the angular overrun atidle and the tool speed is ω_(a) when the applied torque is T_(a).

In an unregulated pneumatic vane motor, the stall torque T_(o) variesapproximately with Δp which is the difference between the absolute airpressure upstream of the tool and atmospheric pressure which is, ofcourse, the equivalent of the gauge pressure upstream of the tool. Thespeed of the tool varies with Δp^(1/2). As shown in application Ser. No.766,429, now U.S. Pat. No. 4,106,570, filed Feb. 7, 1977, a typicaltightening tool used with this invention incorporates an air supplyvalve which is biased toward the closed position by inlet air pressureand moved toward the open position by a solenoid operator. In thissituation, the time required to close the valve after energization ofthe solenoid decreases as gauge pressure increases. This relationship isapproximately Δp^(-1/2). If the line pressure changes, α_(or) remainssubstantially constant while the stall torque T_(o) varies linearly. Onthis basis, the actual tool overrun δα at the mid-point 62 is a measureof the actual stall torque. If:

    T.sub.s =T.sub.o (1+ε)                             (33)

where T_(s) is the actual stall torque in any particular tighteningcycle and ε is the relative change observed in stall torque. It can beshown that: ##EQU13## T_(a) and δα are measured and are accordinglyknown at the mid-point 62. α_(or) and T_(o) are fixed input values. If εis negative, the tool is underperforming and, if positive, the tool isoverperforming.

Although equation (31) is set up on the basis of line pressure changes,it remains meaningful if changes in stall torque are related to lack oflubrication, blade abnormalities or impending bearing failure. Themicroprocessor will in each case calculate ε and, if it is less than aprescribed negative such as -0.25, then a signal is generated toindicate at the operator's station that the tool has underperformed. Iftool underperformance occurs too frequently, as pointed out more fullyhereinafter, this may also be displayed indicating the existance of asystematic problem requiring attention.

In the alternative, let ##EQU14## where α₁ is the angular distance (FIG.3) from T₁ to the shut off point 60. It will be apparent that y₁ is adimensionless number and basically is the ratio of T₄ /T_(o). As shownin FIG. 3, T₄ is the existing torque value at the mid-point shut offlocation 60 while T_(o) is the normal stall torque. It will be seen fromFIG. 4 that y₁ is an inverse function of tool speed. If the time delaybetween the giving of the shut off command and the closing of the valveremains constant, y₁ is a prediction of tool overrun. Since δα is themeasured tool overrun, it will be seen that z₁ is a function of measuredtool overrun while α_(or) is the normal angular overrun of the toolunder no torque conditions. ε₁ will be recognized as a percentage changein tool and control performance.

If ε₁ is low, for example ≦-10%, the deduction is that actual stalltorque has decreased significantly, such as from a loss or decline inair pressure, lack of lubrication, worn or broken parts, or the like. Insuch an event, a signal may be displayed at the tool location toindicate that the tool requires inspection, maintenance, repair orreplacement. It is conceivable, but quite unlikely, that a significantdecrease in ε₁ could be caused by a decrease in time delay between theshut off command and the air valve closing.

If ε₁ is positive, i.e. greater than zero, complications arise. Itappears that z₁, which is a simplification of a more complex equation,loses accuracy. The more complex equation indicates that if ε₁ ispositive, z₁ should be reevaluated as:

    z.sub.2 =δα/α.sub.or.                    (40)

Accordingly, ε should be reevaluated for greater accuracy, whenpositive, as: ##EQU15##

If ε₂ is high, for example ≧+10%, the deduction is that the time delaybetween the shut off command and the air valve closing has decreasedsignificantly or that air pressure supplied to the tool has increased.This normally indicates that the valve control solenoid is beginning tostick or that air pressure is too high. In such event, a signal may bedisplayed at the tool location to indicate that the air control systemrequires inspection, maintenance, repair or replacement. It isconceivable, but quite unlikely, that a significant increase in ε₂ couldbe caused by increased tool efficiency.

As will be apparent to those skilled in the art, the prediction of tooloverrun embodied in equation (37) does not include a measure of overrunbased on inertia, but instead based solely on time delay. As mentionedpreviously, inertial overrun is rather insignificant with moderate tohigh torque rate fasteners although accuracy can be improved somewhatfor low torque rate fasteners by including an inertial overrunprovision. In the event that it is desirable, a measure of inertialoverrun can be incorporated into equation (39) through one or both ofequations (37) or (38).

It is apparent that a single indication of tool malfunction is probablynot significant but that an abnormal frequency of tool malfunction issignificant. Thus, a running ratio of

    C.sub.TL /C.sub.J ≧C                                (42)

is maintained where C_(TL) is the number of times that ε≦-10%, C_(J) isthe number of joints tightened and C is a fraction acceptable to theuser. The ratio C_(TL) /C_(J) is preferably a running ratio, as bystoring on a first-in, first-out basis, rather than a cumulative ratio.From present information, it appears that C should be in the range of0.1-0.2, for example 0.15.

Similarly, a running ratio of

    C.sub.TC /C.sub.J ≧D                                (43)

is maintained where C_(TC) is the number of times that ε≧+10% and D is afraction acceptable to the user, for example, 0.15.

Another approach for predicting tool overrun and thereby detecting toolmalfunction is pointed out by:

    α.sub.p =(1-T.sub.4 /T.sub.o)α.sub.or          (44)

where α_(p) is the predicted tool overrun from the shut off commandpoint 60 where the torque value T₄ appears. The measured value ofoverrun δα from the point 60 can be compared against α_(p), as follows:

    H≦δα/α.sub.p ≧G            (45)

where H and G are values acceptable to the user, such as 0.85 and 1.15respectively. When measured overrun δα is too small, this indicates amotor malfunction while if δα is too large, it indicates a controlsystem malfunction.

Quality Control--Non-linear Strain

Another quality control procedure employed at the mid-point stop 62 isthe detection of non-linear strain, whether elastic or plastic. Ifnon-linear strain occurs before the mid-point stop, it could be detectedby any of the following indirect techniques. First, if the joint isdeeply within the plastic zone, the torque rate calculations will beaskew so that an attempt will be made to search for torque data outsidethe memory. This indirect method is similar to indirectly determiningwhether the torque rate TR is abnormally low and will cause the joint tobe rejected. Second, the joint might be rejected because the observedtorque rate TR is less than the minimum expected torque rate TR_(min).Third, it is possible that the joint will be rejected because thetorque-angle plot is not linear but is instead demonstratably arcuate.In addition to or in lieu of relying on indirect techniques fordetecting excessive non-linear strain, it is desirable to directlydetermine if it has been experienced by the fastener.

To this end, a classic yield point determination is made. Referring toFIG. 5, there is illustrated a torque-angle curve 68 which is intendedto represent a simplification of the showing of FIG. 3. The curve 68terminates at the mid-point stop 62 and describes, in the region 70, atorque rate TR. Ideally, and in accordance with classic yield pointdeterminations, an imaginary line 72 is spaced from the location of meantorque T_(m) and accordingly from the linear region 74 of the curve 68by an offset angle or offset strain α_(y). Although the value of α_(y)may vary as pointed out more fully hereinafter, a typical value to theparticular fasteners disclosed immediately preceding Table II is 12°.

The angular location of T_(m), which is α_(F), is known as shown in FIG.3 and as calculated from equation (17). The angular location of themid-point stop 62 along an abcissa T_(os) +T_(pv) is, of course, theabsolute value of α_(origin).

Thus, a torque value T_(t) on the imaginary line 72 which is used tocompare with the torque reading at the mid-point stop 62 is:

    T.sub.t =T.sub.m +(-α.sub.origin -α.sub.F -α.sub.y)TR. (46)

In the event that T_(t) is less than T_(d), the conclusion is that thejoint has not experienced significant non-linear strain. It will beapparent that the value of T_(d) is suppressed by the act of stoppingrotation. Accordingly, if T_(t) is less than T_(d), there is greatassurance that the joint has experienced no significant non-linearstrain. In the event that T_(t) is equal or greater than T_(d), theconclusion is that the joint has experienced significant non-linearstrain and the joint is rejected. A portion 76 of the torque-angle curveof an unacceptable joint is illustrated as crossing the imaginary line72 at a torque value below T_(t).

The actual digital logic for conducting a non-linear straindetermination in the region surrounding the mid-point and adetermination in the region adjacent the termination of tightening issomewhat complex. Accordingly, a more generalized version may be usedwhich can accomodate both the mid-point and the final determinations.

FINAL SHUT OFF PARAMETER PROCEDURES

It will now be appreciated that the location 62 of calculated tensionF_(o) appearing in the joint corresponds to the point 26 illustrated inthe more general showing of FIG. 1. The determination yet to be made isthe additional angle α_(final) or the additional torque ΔT required toachieve the final desired tension value F_(D). Compared to themanipulations used to assure consistently reliable values for torquerate TR and the angle of tension origin α_(origin), these calculationsare relatively straight forward.

Angle Option

One tightening parameter that may be selected to attain the finaldesired tension value F_(D) is the additional angle α_(final). ##EQU16##F_(o) is, of course, obtained from equations (26) or (27) while F_(M) isthe tension value at the break in the tension-angle curve and isdetermined empirically.

It will be appreciated that the tool overran an angle δα when stoppingat the mid-point 62. It is equally apparent that some amount of tooloverrun will occur approaching the final desired tension value F_(D). Atypical torque-speed curve for an air powered tool is shown in FIG. 4.Since the tool will be slowing down during tightening, it will beapparent that the tool overrun approaching the final desired tensionvalue F_(D) will be less than the overrun approaching the point 62.Defining, ##EQU17## where T₄ is the torque value at the point 60 wherethe initial shut off command was given prior to reaching the stoppingpoint 62, T_(o) is the stall torque of the tool, TR is the calculatedtorque rate and δα is the measured angle overrun approaching the point62. The expected tool overrun dα approaching the final desired tensionvalue F_(D) is:

    dα=δα.sub.a (1-α.sub.final /α.sub.a). (50)

In the alternative, it can be shown that:

    dα=α.sub.or (1-T.sub.4 '/T.sub.o)              (51)

where T₄ ' is the applied torque at the moment of final tool shut off.The overrun δα at the mid-point stop 62 is measured by the angle encoderwhile its theoretical value is:

    δα.sub.t =α.sub.or (1-T.sub.4 /T.sub.o)  (52)

where T₄ is the torque value at the shut off at the point 60 precedingthe mid-point stop 62. Dividing equation (51) by equation (52), arelationship can be found between the two overruns which is independentof α_(or). Accordingly, one can use a semiempirical approach to estimatedα. In order to do so, an estimate of the final torque T_(D) must beprovided.

    if X≧0, T.sub.D =T.sub.sp +uα.sub.final       (53)

    if X<0, T.sub.D =T.sub.sp +uα.sub.final +X(u-TR)     (54)

where

    u=rRTR                                                     (55)

and R is defined as TR₂ /rTR. Consequently, equation (55) reduces to theproposition that u=TR₂.

It can be shown that the semiempirical relationship between final andmid-point overruns is: ##EQU18##

Regardless of how the amount of final overrun dα is determined, the shutoff command to the tool is given at an angle location α_(final) -dα.Overrun of the tool causes the fastener to move to the final anglelocation α_(final). The next problem is where to commence themeasurement of the angle increment α_(final) -dα. The problem has twocomponents: the effect of joint relaxation and the effect of a transientrise in torque during restarting.

It has become apparent that a typical joint will relax, i.e. losetension without unthreading of the fasteners, at the mid-point stop 62and/or at the termination of tightening. If the fasteners werecontinuously tightened, i.e. without a mid-point stop, the relaxation attermination of tightening can be rather significant while, with amid-point stop, the relaxation at termination of tightening is quitemodest. By stopping at the mid-point 62, the bulk of joint relaxationoccurs prior to the resumption of tightening. Thus, the stopping at themid-point 62 provides greater consistency in final joint tensionalthough this phenomenon complicates the determination of the final shutoff parameter, or more correctly, complicates the determination of whereto commence measuring the final angle of advance.

If the joint did not relax at the mid-point stop 62, the tool would beinstructed to go an additional angle α_(final) -dα beyond the mid-pointstop 62 where the final shut off command would be given. As shown inFIG. 1, the final shut off command would occur at about the point 78whereby the tool overruns to tighten the fastener pair through an angledα until stopping at the final desired tension value F_(D).

The phenomenon of joint relaxation is illustrated in FIG. 6 where thecurve 80 represents the tension-angle relationship during continuoustightening to a location 82 below the elastic limit of the fastener.When tightening stops, the joint relaxes as suggested by the tailing offof tension along a constant angle line 84. The final tension appearingin the fastener is accordingly at the point 86. A typical value forjoint relaxation along the line 84 is 7% of joint tension withintwenty-one hours.

Referring to FIG. 7, the curve 88 represents the tension-anglerelationship during tightening to the mid-point stop 62. Because thejoint relaxes, tension in the fastener tails off along a constant angleline 90 to a tension value at the point 92.

One technique for accomodating joint relaxation is, instead ofinstructing the tool to go an additional angle α_(final) -dα from themid-point stop 62, to advance the fasteners an additional angleα_(final) -dα after the running torque equals or exceeds T_(sp) where

    T.sub.sp =T.sub.3 +TR(Δα) in the event that X≦0, or (57)

    T.sub.sp =T.sub.3 +u(Δα) in the event that X>0. (58)

T_(sp) will be recognized as the calculated torque value which would beexpected at the mid-point 62 except for the effect of stopping. It willbe recollected that the torque value T₃ is located at the point 64,which is one Δα backward from the mid-point stop 62. By advancing thetool until running torque equals or exceeds T_(sp), the torque andtension values at the mid-point stop 62, before relaxation occurs, areessentially reproduced. This is indicated in FIG. 7 where the point 94designates the location where running torque is equal to or greater thanT_(sp). Tightening will then be done correctly, regardless of prevailingtension in the bolt at the time the tool resumes tightening. As shown inFIG. 7, the final shut off command occurs at the point 96 whereby thetool overruns to tighten the fastener pair through an angle dα untilstopping at the final desired tension value F_(D). In order to shift thebulk of joint relaxation from the final stopping point to the mid-pointstop 62, the mid-point stop is at least 0.4 of yield strength andconveniently is in the range of 0.4-0.75 yield strength. With themid-point stop 62 so located, typical joint relaxation at the finalstopping point is on the order of 1/2-2% of final bolt tension withinone hour. It should be clear that this amount of joint relaxation is therelaxation of a good quality joint rather than a joint suffering frommisaligned parts, compressed gaskets and the like.

Although measuring the angle of advance from T_(sp) provides betterresults than merely measuring the advance from the mid-point stop 62,the results can be further improved upon. Accordingly, a preferredtechnique for accommodating joint relaxation, accommodating a transienttorque rise immediately on restart and to take up any gear-socketbacklash is to advance the fasteners the additional angle α_(final) -dαafter the running torque equals or exceeds a value slightly greater thanT_(sp). This transient torque rise is caused by static friction and/orthe change over from static to dynamic in much the same manner that thetorque peak 30 is generated at the onset of tightening as shown in FIG.2. The amount of T_(sp) should be increased is subject to compromise andis somewhat arbitrary. In the absence of joint relaxation, the transienttorque rise has been observed to lie between 0-15% above the expectedtorque. Accordingly, a compromise adjustment of 8% is preferred so thatthe measurement of the angle α_(final) -dα is preferably measured from1.08T_(sp). In the absence of joint relaxation, the transient torquerise is so fast that essentially only the backlash in the tighteningtool is taken up, regardless of any compensating factor in the range of0.9-1.1. In other words, in the absence of joint relaxation, essentiallyno angle error is created in restarting the tool and measuring the angleof advance from T_(sp). When joint relaxation occurs, however, thecompensating factor is material.

Torque Option

Another tightening parameter that may be selected to attain the finaldesired tension value F_(D) is the additional torque ΔT or the finaltorque T_(D) (FIG. 1). The final torque T_(D) is preferred since thejoint may relax at the mid-point stop 62. Because the tool instructionis to achieve an absolute torque value T_(D), any relaxation in thejoint is automatically accomodated. In using a torque governed shut offparameter, even a possible tightening of the joint at the mid-point stopwill also be automatically compensated for.

In using a torque governed shut off, an interesting phenomenon has beennoted for which no simple explanation appears. Referring to FIG. 1, itwill be noted, as previously mentioned, that the tension rate FR₂ isgreater than the tension rate FR₁, typically by 5-15% depending mainlyon the value selected for F_(M). This would lead one to believe that thetorque rate in the region 20 would be greater by a similar amount thanthe torque rate in the region 18. Laboratory investigations indicatethat the torque rate in the region 20 typically exhibits a slightlysmaller increase over the torque rate in the region 18. Fortunately, theratio of the torque rates in the regions 18, 20 to the ratio of thetension rates FR₁, FR₂ is more nearly constant for a single typefastener pair. In calculations for a final torque shut off command, thisfactor is taken into account, as follows: ##EQU19## where T_(MC) is acalculated value for the torque at the break in the tension curve, R isdefined as TR₂ /rTR, TR₂ is the torque rate in the region 20, TR is thetorque rate in the region 18, and r is the ratio of FR₂ /FR₁.

As is the case in the angle governed final shut off calculations, thetool will overrun after the final shut off command. Defining,

    δT=TR.sub.2 (dα)                               (61)

    T.sub.a =T.sub.o -T.sub.4 -δT                        (62) ##EQU20## where dα is a calculated value for angle overrun from equation (50), (51) or (56). In the alternative,

    T.sub.b =T.sub.D -TR.sub.2 dα                        (64)

where T_(b) is the torque value at shut off.

After tightening is resumed, the final shut off command is given eitherwhen running torque T≧T_(b) or T_(D) -dT. As shown in FIG. 1, the finalshut off command will occur at about the point 78 whereby the tooloverrun continues to tighten the fastener pair for an additional torquevalue dT until stopping at the final desired tension value F_(D).

It is apparent that tightening of the fastener pair can be terminated inresponse to calculated tension which is derived by the techniques ofthis invention. Upon analysis, it will be evident that terminatingtightening in response to calculated tension is in reality the same asterminating tightening in response to either angle or torque, dependingon how the calculations of tension are conducted.

Torque--Angle Option

It will also be apparent that tightening may be terminated in responseto a combination of torque and angle, for example, a linear combinationof torque and angle. Assuming that one wished to equally weigh thecalculated advance derived from the torque and angle computations, theappropriate equation is generically: ##EQU21## where F_(o) is thecalculated tension value at the mid-point stop 62 as may be calculatedfrom equation (26) or (27) depending on whether X≦0 or X>0, and T_(sp)is the calculated torque value at the mid-point stop 62 as may becalculated from equation (57) or (58) depending on whether X≦0 or X>0.The calculations for α_(final) will depend on whether X≦0 or X>0 aspointed out in equations (47) and (48). Calculations for T_(D) are madeusing equations (53) and (54).

As with the use of other tightening parameters, it is desirable toprovide an overrun correction. It is apparent that the angle overruncorrection of equation (50) may be incorporated as an overrunprediction, as follows:

    F.sub.or =r(FR.sub.1)dα                              (66)

where F_(or) is the increase in tension due to overrun. It may also bedesirable to use an equally weighted linear combination of torque andangle in determining the predicted tool overrun. The tension produced inthe bolt during overrun may be calculated as: ##EQU22##

It will be apparent that one cannot merely instruct the tool to proceedan additional angle or until a desired torque level is reached in orderto stress the bolt to the desired tension value F_(D) when using a mixedparameter of torque and angle. Instead, one may calculate the tensionappearing at any angular position α₃ beyond the point 62 as ##EQU23##where T.sub.α.sbsb.3 is the sensed torque value at the angular positionα₃, T_(sp) is the calculated torque value at the mid-point stop 62, andT_(MC) is the calculated torque value at the location of F_(M) accordingto equation (59).

The calculated tension value at the point of shut off is:

    F.sub.so =F.sub.D -F.sub.or                                (70)

where F_(D) is from equation (65) and F_(or) is from equation (67). Bycomparing the value of F.sub.α.sbsb.3 at angle increments, such as Δα,1° or the like, with F_(so), as soon as F.sub.α.sbsb.3 ≧F_(so), the shutoff command is given. In this fashion, tightening may be terminated inresponse to a linear combination of torque and angle.

PROCEDURES INVOLVING RESTARTING OF THE TOOL Decision to Advance

It is evident that the tension achieved in the fastener at the mid-point62 may be substantially less than F_(D), equal to or very close to F_(D)or greater than F_(D). If the tension F_(o) achieved at the mid-point 62is greater than or equal to F_(D), the tool is not restarted but isinstead reset to commence the tightening of the next fastener. In thiscircumstance, it may be desirable to provide an indication that thejoint is satisfactorily tightened provided that the previously conductedquality control operations indicate that the joint is acceptable.

Accordingly, the question is whether to restart the tool when themid-point tension F_(o) is less than F_(D). Using, for purposes ofillustration, the angle option technique for advancing the tool, if

    α.sub.final -dα>0                              (71)

the tool is instructed to advance the angle increment α_(final) -dαafter either T_(sp) or 1.08T_(sp), depending on the election on how tohandle joint relaxation. If α_(final) -dα=0, the tool is instructed tocommence turning and the shut off command is given immediately uponobserving T_(sp) or 1.08T_(sp). If, however, α_(final) -dα<0, twodecisions are possible. The value of dα is normally greater than zero.Accordingly, if

    dα<2α.sub.final                                (72)

then the tool is instructed to open the air supply valve and issue ashut off command upon observing either T_(sp) or 1.08T_(sp). Otherwise,the best available final tension is the mid-point value F_(o).

Torque Signal Filtering

There are many tools, for example the tool illustrated in copendingapplication serial number 766,429, now U.S. Pat. No. 4,106,570 that donot exhibit any substantial internal chattering which is reflected asnoise in the torque signal. There are, however, a number of tools inwhich internal chattering produces undesirable noise in the torquesignal. One such tool is of the type having the tool output angularlydisposed relative to the motor shaft. In tools of this type, a set ofmeshing gear teeth effect the inclination of the output drive. In thissituation, the meshing gear teeth apparently produce the noise that isreflected in the torque signal. It is desirable to filter the torquesignal to reduce this noise. The difficulty is that a filter which willremove noise caused by internal chatter tends to slow the time responseof the torque signal during startup for the final advance and causesresponse time problems near the termination of tightening.

To overcome these difficulties, there is preferably employed a pair offilters which are placed in circuit with the torque sensor by a switchcontrolled by the microprocessor. The first filter, which isconveniently of the resistance-capacitance type, has a substantialcapacitance and accordingly acts to substantially filter the torquesignal. The processor controls the switch to place the first filter incircuit with the torque sensor during the initial part of the tighteningcycle, usually up to and including the mid-point stop 62. At themid-point, the first filter is switched out of circuit with the torquesensor and a second filter is placed in circuit therewith. The secondfilter may also be of the resistance-capacitance type and has a muchlower capacitance. The second stage filtering merely eliminates any veryhigh frequency noise.

The difficulty with this approach is that the initial heavy filteringwill cause a predictable torque-angle distortion that fortunately can becompensated for during the joint set up procedure. The other problemswith filtering the torque signal is that deterioration or failure of thefilter would cause tension errors.

NON-LINEAR STRAIN PROCEDURES DURING THE FINAL ADVANCE

Referring to FIG. 8, another feature of the invention is illustrated.When tightening to the final desired tension value, it is highlydesirable to assure that the yield point is not reached or is at leastnot substantially exceeded. This may be done graphically as shown inFIG. 8 by drawing a line 98 parallel to the torque curve 10 in theregion 20 or parallel to the tension curve 12 and spaced therefrom by anangle α_(y) in accordance with the classic offset strain technique. Thevalue of α_(y) can be correlated with an acceptable amount of strain inthe bolt since the amount of nut rotation in this region of the torquecurve can be calculated into a percentage of bolt elongation because ofthe known pitch of the threads. When the running torque value Tintersects the line 98 at the point 100, the tool is given a shut offcommand and ultimately comes to rest at a point 102 because of tooloverrun.

In order to implement this technique, the torque value sensed by thetool is monitored after the tool is turned on again after the mid-pointstop 62. One difficulty arises since the restarting torque applied tothe fastener in order to resume tightening typically is relativelysubstantially larger than the running torque immediately prior to themid-point stop 62 as is caused by the difference between the static anddynamic coefficients of friction and complicated dynamic factors. Whenthe sensed value of running torque T first equals or exceeds the valueof T_(M) where:

    T.sub.M =T.sub.3 +TR(Δα-X)                     (73)

this location is marked and two Δα increments beyond this location,which is location 104, the running torque T is sensed and stored as T₅.T_(M) will be recognized as a calculated torque value which appears atthe location on the torque-angle curve corresponding to the break in thetension curve.

As is apparent from FIG. 8, the calculations being done to detect theyield point or, in the alternative, an amount of non-linear strain belowthe yield point, occur in the region 20 where the torque rate issomewhat lower than the torque rate value calculated in the region 18.The torque rate in the region 20 can be expressed in accordance withequation (55).

Yield or non-linear strain calculations can be conducted periodicallyduring tightening in the region 20 as often as is deemed desirable.Although the calculations can be done at every angle increment Δα,results are quite satisfactory if done every other angle increment Δα.According,

    ΔT.sub.1 =2u(Δα)                         (74)

    ΔT.sub.y =uα.sub.y                             (75)

where α_(y) is the angle corresponding to a desired strain level whichcan either be elastic but non-linear or plastic, ΔT₁ is the incrementaltorque over the incremental angle 2Δα and ΔT_(y) is the incrementaltorque over the incremental angle Δ_(y). By selecting small values forα_(y), the shut off command will tend to be in the elastic butnon-linear range below the yield point. If α_(y) is selected to ba alarge value, the shut off point will appear in the plastic range abovethe yield point. It is thus apparent that the detection of non-linearstrain can encompass both elastic and plastic strain. The onlydifficulty is selecting very small values for α_(y) is that noise in thetorque curve 10 in the range 20 might create a premature and false yieldsignal. At a point 106, which is two Δα degrees after the occurrence ofT₅, the value of running torque T is compared with

    T.sub.y1 =T.sub.5 -ΔT.sub.y +ΔT.sub.1          (76)

It is apparent that T_(y1) is a torque value on the line 98 at the point108. It T>T_(y1), tightening continues. At a point 110, which is two Δαdegrees beyond the point 106, the value of running torque T is comparedwith ##EQU24## If T>Ty₂, tightening continues. This procedure continuesby adding an additional torque value ΔT₁ to the preceding value of T_(y)at angle increments of two Δα. In the event that T≦T_(y) before theoccurrence of the shut off command derived from the normal tighteningparameter of torque or angle, a shut off command is given to the tool.It will be apparent that the actual shut off command from detection ofnon-linear strain or the actual detection of non-linear strain will notoccur at exactly the point 100 since comparisons are being made everytwo Δα. Thus, the actual yield detection will probably occur later, e.g.at the point 112 as shown in FIG. 8.

Thus, tightening is normally terminated in response to a torquegoverned, an angle governed or a mixed shut off command, but in the caseof yield point detection or, in the alternative, detection of non-linearstrain below the yield point, a premature shut off command is given. Itwill accordingly be apparent that the upper end of the scatter band iseliminated by a secondary yield point shut off. Thus, the total scatterwill be reduced. It will also be apparent that the detection ofnon-linear strain may be conducted as disclosed in U.S. Pat. Nos.3,643,501 or 3,693,726, although the technique herein disclosed isdeemed preferable.

It will be appreciated that the non-linear strain detection conducted atthe mid-point stop 62 is conceptually the same as the determination madeduring tightening toward the final desired tension value. The details ofthe determination as here disclosed are somewhat different. In order tosimplify the program, it may be desirable to utilize a common approach.

It has been discovered that tightening can be consistently terminated inresponse to non-linear strain in the elastic region provided thatcertain precautions are taken. It is essential that a reliable value beobtained for the average torque rate of the fastener being tightened.Necessary to obtaining a reliable torque rate is conducting thecalculations over an angle increment of significant size relative to theangular distance between the origin of stress and the proof load of thefastener. Typically, the minimum angle increment over which torque ratecalculations are conducted should be in the range of 10-20% of thisangular distance. Torque rate determinations made over smaller angleincrements tend to be unduly influenced by noise in the torque signal.Another desirable feature is avoiding a two point torque ratecalculation and instead using an averaging technique using at least 5and preferably 10 different data points in order to minimize the effectof a single unusual torque sensing on the calculated torque rate. Theapproach of this invention is particularly suited to terminatingtightening in response to non-linear strain in the elastic zone becauseof the pains taken to obtain a consistently reliable average torquerate. It will be appreciated that this feature is of considerableimportance because of the desire of joint designers to achieve hightension stresses in the bolts without advancing threading into the zoneof plastic deformation.

PROCEDURES AT TERMINATION Frequency of Shut Off Due to Non-linear Strain

It is preferred that the selection of F_(D) will be low enough so thatthe cutoff due to detection of non-linear strain will be rare, e.g.0.1%. in the event that the percentage of premature tighteningtermination due to non-linear strain detection rises substantiallyduring a production run, this indicates that the fasteners, i.e. boltsand/or threaded parts, employed do not meet design specifications.Accordingly, a high percentage of non-linear strain detections is asignal that quality control investigations need to be conducted on thefasteners employed. For example, if the normal occurrence of non-linearstrain is on the order of 0.1%, and a running average of non-linearstrain detections is 10%, it is likely that the fasteners being run donot meet specifications.

To identify batches of fasteners which do not meet specifications, arunning count of the number of joints tightened is maintained and arunning count of the number of joints exhibiting non-linear strain ismaintained. A frequency determination is accordingly made, as follows:

    C.sub.Y /C.sub.J ≧A                                 (79)

where C_(J) is the number of joints tightened, C_(Y) is the number ofjoints experiencing non-linear strain and A is some fraction acceptableto the user. From present information, it appears that the value of Ashould be in the range of 0.10-0.20, e.g. 0.15. The ratio of C_(Y)/C_(J) is preferably a running ratio, rather than a cumulative ratio, asby storing, on a first-in, first-out basis, a finite number of jointstightened C_(J), e.g. 30, and any instances of non-linear straindetection C_(Y). When the running ratio of C_(Y) /C_(J) equals orexceeds the selected value A, a suitable signal may be providedindicating that the frequency of non-linear strain is much too high. Theinvestigations to be conducted normally include analysis of the strengthand material composition of the fasteners, a technique well known in theart.

When To Conduct Extensive Quality Control Procedures

It will be appreciated that termination of tightening may occurnormally, i.e. in response to the final shut off parameter, may occur inresponse to the detection of non-linear strain during tightening towardthe final shut off parameter, may occur because the mid-point tensionF_(o) is too close to the final desired tension value F_(D) or may occurin response to one of the quality control procedures done at themid-point 62. If tightening is terminated because the mid-point tensionT_(o) is too close to F_(D) so that the tool cannot be restarted, one oftwo conclusions can be reached: (1) the joint has an unusually low valuefor torque rate TR and should be rejected or (2) the joint is acceptableprovided that F_(o) passes the final tension check discussedhereinafter. The decision depends on the other quality controlprocedures conducted at the mid-point 62 and the decision of the systemdesigner. In the circumstance where tightening is terminated because thejoint is rejected by one of the quality control procedures, nothingfurther needs to be done. Accordingly, there are two situations whereextensive quality control procedures are desirable, i.e. when tighteningis terminated normally and when tightening is terminated in response tothe detection of non-linear strain occurring after the mid-point stop62.

Final Tension Determination in the Elastic Zone

It is desirable to calculate and store the final tension appearing in afastener, the tightening of which is terminated normally, i.e. inresponse to torque and/or angle rather than non-linear strain. Whenusing a torque approach, equation (87) gives a value for F_(final)regardless of whether yield has occurred or not. When using an angleapproach, the final achieved tension value may be calculated from:

    F.sub.final =F.sub.D -rFR.sub.1 (α.sub.final -α.sub.actual) (80)

where α_(actual) is the actual measured angle increment between theT_(sp) or 1.08T_(sp) and the final stopping point.

Final Tension at Tool Stall

It is also desirable to calculate and store final tension appearing in afastener in other circumstances, such as when the tool stalls. Toolstall may occur before the mid-point stop 62 or after. Before themid-point stop 62,

    F.sub.final =F.sub.o.                                      (81)

After the mid-point stop 62, the final desired tension value F_(final)may be calculated using a torque approach as: ##EQU25## where T_(sp) isthe calculated torque at the mid-point stop by equation (57) andT_(final) is the last highest torque sensing obtained within one or twoΔα increments of the final stopping point.

After the mid-point stop 62, the final desired tension value F_(final)may alternatively be calculated, using an angle approach, as:

    F.sub.final =F.sub.o +rFR.sub.1 α.sub.actual, where X>0 (83)

where α_(actual) is the actual measured angle from T_(sp) or 1.08T_(sp)to the final stopping point.

Non-linear Strain Detection

This is a theoretically redundant check on the possible occurrence ofexcessive non-linear strain. The joint is rejected or indicated ashaving experienced excessive non-linear strain in the event that:

    T.sub.final ≦T.sub.m +TR(-Δ.sub.origin -α.sub.F)+u(α.sub.actual -α.sub.y)      (84)

where T_(m) is the mean torque value at the angle location α_(F). Itwill be recollected that α_(origin) is a negative value therebyrequiring the minus sign. The technique is basically to add a calculatedtorque value to the mean torque T_(m) to obtain a calculated torquevalue at the mid-point stop and then add another calculated torque valuerepresenting the additional increase in torque from the mid-point stopto the final stopping place which occurs at the angle α_(actual). Ifthis calculated value is equal to or greater than the highest torquesensing T_(final) obtained within one or two Δα increments of the finalstopping place, the joint is flagged.

Final Tension Determination in the Plastic Zone

It is highly desirable to calculate and store the final tensionappearing in a fastener which has been stopped prematurely because ofnon-linear strain detection. It may be that the final tension valueachieved is well within an acceptable range. In this event, it would bedisadvantageous to require removal and replacement of the fastener pairif the problems associated with marginally yielded fasteners are notmaterial if the fasteners are sufficiently stressed to assure acceptablejoint conditions.

Accordingly, when using an angle approach, the value of final tensionmay be calculated as follows:

    T.sub.final =F.sub.D -rFR.sub.1 (α.sub.actual +α.sub.y -α.sub.2)                                           (85)

where α₂ is the angle from the stopping point 102 to the location whereyield detection is sensed. It will be appreciated that any calculatedvalue of F_(final) is somewhat of an approximation since the tensionrate well above the proportional limit is unknown and perhaps unknowablewith any degree of accuracy. FIG. 9 graphically illustrates thedifficulty. If the final tension value were calculated:

    F.sub.final =F.sub.D -rFR.sub.1 (α.sub.final -α.sub.2) (86)

the tension actually being calculated would be at the point 114 which isat the same angular position α₂ from the stopping point 102 as the yielddetection point 112. It will be appreciated that the difference intension values between the points 112, 114 may be significant in somecircumstances. Since it is known that the tension rate falls offsubstantially immediately prior to the point 100, it is safe tocalculate the tension value at the point 116 which is spaced downwardlyalong the slope FR₂ by an angular distance α_(y). Thus, the rationalefor the equation (86) is apparent. It will be appreciated that theactual final tension appearing in the joint is that at the point 112which differs from the calculated tension value appearing at the point116. It will be seen, however, that the tension value at the point 116is a substantially better estimation of actual final tension than is thetension that would be calculated at the point 114. This is particularlytrue since the tension rate in the range 118 is known to be quite low.The final tension value F_(final) along with a notation that the bolthas yielded may be displayed at the tool location, printed or otherwiserecorded for further use or analysis.

In the event the torque governed final shut off parameter is being used,when T≦T_(y), non-linear strains is detected and a shut off command isgiven the tool. The final tension value may be calculated from a torqueapproach, as follows: ##EQU26## where T_(final) is the highest value oftorque sensed within one or two Δα increments before the final stoppingplace 102. This is likewise illustrated in FIG. 9. The detection ofyield occurs at point 112 on the torque curve 10 which the point 102being the final stopping point. The torque at the point 102 isunreliable for the same reasons that the torque reading at the mid-pointstop 62 is unreliable. Accordingly, the torque value T_(final) is takenas the peak within one or two Δα increments backward from the point 102,such as at the point 120. The effect of this, graphically is shown bythe horizontal line 122 terminating on the torque slope TR₂ at the point124 and the vertical line 126 terminating at the point 128 on thetension slope FR₂. Thus, the final tension value F_(final) is thecalculated tension at the point 128.

In the alternative, the following estimate is fairly accurate: ##EQU27##where T_(mm) is T_(sp) provided that T_(sp) ≧T_(mm), where T_(mm), isT_(m) +TR(-α_(origin) -α_(F)). It T_(sp) <T_(mm), then T_(mm)=TR(-α_(origin) -α_(F)).

In the event the tool continues to run far beyond any reasonable angleof advance, the conclusion is that the bolt has failed without yielddetection, as may occur before the mid-point stop 62. Thus, noappreciable tension appears in the bolt and

    F.sub.final =0.                                            (89)

Final Tension Check

In any circumstance where F_(final) is calculated, it may be desirableto compare it with the final desired tension value F_(D). In this event,if ##EQU28## where B is a fraction deemed acceptable to the user, asuitable signal may be displayed to indicate that calculated tension issubstantially below desired tension. From present information, itappears that the magnitude of B should be greater than the expectedscatter from use of this invention and preferably should be 3-4 normaldeviations. Thus, B should be in the range 0.10-0.17.

Final Tension Consistency Check

Another approach of this invention is to normally terminate tighteningin response to one parameter, e.g. torque, and check this shut offparameter against another shut off parameter, e.g. angle. If the resultscompare closely, this is an indication that the assumptions made, theempirically determined joint parameters and the like are reasonablycorrect. If the comparisons are significantly different, this is anindication that something is amiss and that the operation should bestopped or investigations instituted to determine the cause. When usingtorque as the tightening parameter, F_(D) has been placed in thecalculations for the final torque value T_(D) by equation (53) or (54)depending on whether X≧0 or X<0. The calculated value of final tensionF_(final) using an angle approach at a final angle of advance ofα_(final) is:

    F.sub.final =F.sub.D -rFR.sub.1 (α.sub.final -α.sub.actual) (91)

where α_(actual) is the angle of advance from T_(sp) or 1.08T_(sp) tothe final stopping point. If the different between F_(D) and F_(final)is small, e.g., ±5-10%, it is apparent that substantial confidence maybe placed in the technique. If the difference between F_(D) andF_(final) is larger, e.g. ±20%, it is apparent that something is amissand that the tightening operation should be stopped or investigationsinstituted to determine the cause.

Final Torque Consistency Check

Assuming that the final advance of the fastener was determined in termsof angle and the joint has not experienced non-linear strain, a check ofthe value of the actual final peak torque T_(final) against a calculatedvalue of the expected final torque T_(D) provides an independentevaluation of the procedures. In order to make this determination,preliminary calculations are made. First, the actual attained finaltension value F_(final) differs from the expected tension value F_(D)only if the actual amount of tool overrun is different from the estimatedα. The actual attained tension value is

    F.sub.final =F.sub.D +(α.sub.actual -α.sub.final)rFR.sub.1 (92)

where α_(actual) is the actual observed angle from T_(sp) or 1.08T_(sp).This calculation will provide a value for actual attained tension forF_(final). Realizing that the actual attained tension value F_(final)will differ from F_(D), a correction is made in the expected value offinal torque T_(D), as follows:

    T.sub.D '=T.sub.D F.sub.final /F.sub.D                     (93)

where T_(D) ' is the revised value of T_(D). The value of T_(D) ' mustbe comparable with T_(final). A torque-angle consistency factor η_(T) isthen defined as ##EQU29## Ideally, η_(T) should be zero. It will beappreciated, however, that minor deviations in η_(T) from zero are notindicative of any substantial problem. In good quality joints, it hasbeen found that values of η_(T) on the order of about 0.13 rarely givefalse indications of defective joints. Accordingly, this value is used.If a better value is available, it should be used instead. Thus, a jointis judged defective in the event that

    -0.13≦θ.sub.T ≧0.13,                   (95)

the tool is reset for the next tightening cycle and a signal is giventhat the joint has failed. In the event that parts quality is known tobe subnormal, the value of η_(T) should be increased somewhat.

This quality control procedure causes the rejections of jointsexperiencing thread galling, joint where the mid-point analysis, forsome reason, is performed in a very low tension range, joints whichyield and the non-linear strain procedures do not detect if, jointstightened with faulty torque or angle instrumentation, or jointstightened with incorrect input parameters fed to the microprocessor.

Final Torque Rate Consistency

This quality control procedure is intended to provide additionalinsurance against a fairly flat torque-angle curve near the terminationof tightening which may possibly indicate significant penetration of theplastic zone somehow not detected by other routines. In this procedure,the final torque rate is checked against the empirically determinedtorque rate u or TR₂ within the angle interval of actual tool overrun.Defining, ##EQU30## where T_(marker) is the torque sensing art the shutoff command and T_(final) is the peak torque value sensed in the lastfew Δα increments prior to stopping. If FRC is less than some suitablevalue, e.g. 0.25, the joint is indicated as failing this procedure. Thisprocedure has its difficulty because the value of T_(final), which isthe peak value of torque within one or two Δα increments from the finalstopping point, is influenced by the act of stopping rotation for thesame reason that the last torque readings prior to the mid-point stop 62are suspect. Experience indicates that if joints are rejected whenFRC<0.25, there is a false indication of joint inacceptabilityapproximating a 1% frequency. This is believed to be caused in largepart by the suspect value of T_(final). The procedure does, however,have its value in providing considerable assurance against prematureyielding if that is of paramount concern to the user.

Frequency of Joint Rejections

It is desirable to indicate a parts integrity problem when the number ofjoints that have failed at least one of the quality control proceduresis too frequent. In other words, the joint failure frequencydeterminations are desirably merged into one single frequencydetermination. The difficulty to be avoided is, of course, countingtwice a joint which fails two of the quality control procedures. Undernormal circumstances, this is not a substantial problem because thequality control procedures are conducted sequentially and notsimultaneously. Accordingly, any joint that fails a single test causesthe cycle to terminate and the cool to be reset for the next succeedingtightening cycle. Accordingly, when ##EQU31## a signal is generated toenergize a parts integrity indicator, where C_(FTR) is the number offailures of the final torque rate check, C_(TRC) is the number offailures of the torque rate curvature check, C_(TRL) is the number ofoccurrences where the torque rate is too low, C_(NM) is the number offailures of the non-linear strain determination at the mid-point stop62, C_(NLS) is the number of times that tightening is terminated inresponse to non-linear strain rather than in response to the normaltightening parameter, C_(NF) is the number of failures of the finalnon-linear strain determination, C_(F) is the number of failures of thetension check, C_(TC) is the number of failures of the tensionconsistency check, C_(FT) is the number of failures of the final torqueconsistency check, C_(J) is the number of joints tightened and J is afraction acceptable to the user. It will be apparent, of course, that anumber of these quality control procedures may be omitted from anyparticular application and consequently will have no bearing on thisfrequency check. It is preferred, as in other frequency checks, thatC_(J) be a finite running number of joints stored on a first in, firstout basis. The quantity selected for this finite number should besufficiently large to avoid statistical aberrations and accordingly ispreferably on the order of 50-500. The value of J is inversely relatedto the selected quantity of C_(J) in the sense that the higher the valuefor C_(J), the lower may be the selected value of J. From presentinformation, it appears that J should be on the order of about 0.05-0.20and is preferably about 0.10 to avoid giving false indications of asystematic parts problem when none exists.

Repair of Failed Joints

When a joint is rejected by the tightening technique of this invention,it is highly likely that at least one part constituting the joint is notup to specifications. In such cases, it is highly desirable thatdefective parts be replaced and the tightening process repeated.However, if the user so wishes, rejected joints can be automaticallytightened to a different parameter and the shut off command given.Because of the stored values of torque and angle, it is conceivable thatthe repair technique could comprise a turn-of-the-nut approach so thatthe tool could be instructed to advance a predetermined number ofdegrees beyond a particular torque location. It appears, however, that aturn-of-the-nut approach is not the most desirable for repairing failedjoints. Instead, it is preferred that the rejected joints be tightenedto a specified minimum torque and the shut off command given. Because ofoverrun, the final torque achieved would be somewhat greater than theminimum specified. This could, of course, be accomodated by making asimple overrun prediction along the lines of equation (64). It isapparent that this procedure is applicable to joints tightened inaccordance with this invention using either the torque or angle optionor tightened in accordance with a turn-of-the-nut strategy.

Shear Joint Routine

In joints which are subjected to significant axial loads, i.e. loadsparallel to the bolt axis, the only object of tightening is to induce adesired tensile stress in the bolt. This is not precisely true in jointswhere all or a substantial fraction of the external load is transverse,i.e. in a plane perpendicular to the bolt axis. In shear joints of thistype, it is desirable from the standpoint of joint mechanics to assurethat a minimum torque value has been applied in addition to assuringthat the bolt stress is above a predetermined value. Accordingly, atypical fastener in a shear joint might be tightened to 90% proof and 40foot pounds. Calculations are conducted in accordance with the previousdisclosure to terminate tightening at 90% proof. If the estimated oractual torque value at the termination of threading advance or one ortwo Δα increments prior thereto is less than the minimum predeterminedtorque, the tool is restarted until the minimum torque value isattained. Accordingly, if the final estimated torque T_(D) or the finalpeak torque T_(final) is equal to or greater than the minimum torqueT_(min), tightening is terminated normally. On the other hand, if theestimated final torque T_(D) or the peak torque T_(final) is less thanT_(min), a value of shut off torque T_(sh) is calculated as

    T.sub.sh =T.sub.min -udα.                            (98)

The tool is accordingly restarted and the air supply valve is closed ata location where the running torque value is T_(sh). The tool overrunsfor an angle increment dα so that the final attained torque value isT_(min).

Joint With Multiple Fasteners

When tightening seriatim a multiplicity of fasteners comprising part ofa single joint using a conventional technique, it is well known that thefirst tightened fasteners will lose at least some tension by the timethe last fasteners are tightened. This is, of course, related to jointrelaxation and alignment of the joint parts. In accordance with thisinvention, one powered instructable tool as disclosed more fullyhereinafter may be used for each fastener and used in the followingmanner.

The tools are started simultaneously. When all of the tools have stoppedat the mid-point 62, all the tools are restarted simultaneously toaccomplish the final advance. In this manner, the alignment of all thefasteners and all joint relaxation occurs at the mid-point stop 62. Eachtool would then compensate for any relaxation that may have occurredadjacent the fastener coupled thereto. It will be apparent that thecontrol mechanism for the tools would be interconnected electronicallyin a fashion that will be apparent to those skilled in the art followingthe more complete description of the tool hereinafter.

EQUIPMENT

Referring to FIG. 10, there is illustrated a schematic showing of amechanism 126 for performing the previously described technique. Themechanism 126 includes an air tool 128 connected to an air supply 130and comprising an air valve 132, an air motor 134 having an output 136coupled to the fastener pair comprising part of the joint 138, a torquetransducer 140 and an angle transducer 142. The torque transducer 140 isconnected to a signal conditioner 144 of a data processing unit 146 by asuitable electrical lead 148.

The signal conditioner 144 is designed to receive electrical signalsfrom the transducer 140 and modify the voltage and/or amperage thereofinto a form acceptable by an analog-to-digital converter 150 through asuitable connecting circuit 152 described more fully hereinafter. Theconverter 150 changes the analog signal received from the conditioner144 into digital form for delivery to an interface logic unit 154through a suitable connection 156. The angle transducer 142 is connectedto the interface logic unit 154 by a lead 158.

The connecting circuit 152 provides the torque signal filtering functiondiscussed. To this end, the circuit 152 includes a pair of parallelleads 158, 160 connecting the signal conditioner 144 to the analog todigital converter 150. The lead 158 is connected to a ground 162 by alead 164. The lead 160 includes a resistor 166. Extending between theleads 158, 160 is a lead 168 having a first capacitor 170 therein. Asecond lead 172 also extends between the leads 158, 160 and has thereina second capacitor 174 as well as a switch mechanism 176 of a relay 178.The relay 178 may be of any suitable type and is designed, whenenergized, to close the switch mechanism 176 to place the secondcapacitor 174 in parallel with the first capacitor 170 in the connectingcircuit 152.

In operation with the relay 178 unenergized, the resistance 166 and thefirst capacitor 170 act as an R-C filter to remove very high frequencynoise from the conditioned torque signal passing across the leads 158,160. When the relay 178 is energized, the second capacitor 174 is placedin parallel with the first capacitor 170. Together, the resistor 166 andthe capacitors 170, 174 act to filter the analog torque signal appearingin the leads 158, 160. As mentioned, the circuit 152 is employed withtightening tools which produce a substantial amount of internal chatter.In such tools, the relay 178 is energized during an initial portion ofthe tightening cycle, usually up to and including the mid-point stop 62.Accordingly, the resistance-capacitance network provided by the resistor166 and the capacitors 170, 174 act to substantially filter the analogtorque signal appearing on the leads 158, 160. At the mid-point stop 62,the energizing signal delivered to the relay 178 is terminated so thatthe switch mechanism 174 opens to remove the capacitor 176 from theconnecting circuit 152.

It will be appreciated that the relative sizes of the resistor 166,first capacitor 170 and second capacitor 174 control the degree offiltering actually accomplished. Although the design of the filteringnetwork is subject to design selections, the following sizings haveproved acceptable: the resistance of the resistor 166 is 2000 ohms, thecapacitance of the first capacitor 170 is 0.5 microfarads, and thecapacitance of the second capacitor 174 is 5 microfarads.

The interface logic unit 154 comprises an interface logic section 180designed to handle information and is connected through suitableconnections 182, 184 to a microprocessor unit 186 which is in turnconnected to a data memory unit 188 and an instruction memory andprogram unit 190 through suitable connections 192, 194, 196, 198. Theinterface logic section 180 is also designed to receive input parameterssuch as T_(os), FR₁, r, F_(D) and the like.

The interface logic unit 154 also comprises an amplifier section 200controlling a solenoid (not shown) in the air valve 132 through asuitable electrical connection 202. The amplifier section 200 alsocontrols a display panel 204 having suitable signal lights through anelectrical connection 206 as will be more fully explained hereinafter.The relay 178 is similar energized through a connection 208 from theamplifier section 200.

The air tool 128 may be of any type desired such as a Rockwell model 63Wwhich has been modified to reduce the amount of overrun or such as isshown in copending application Ser. No. 766,429. It has been surprisingto learn that the bulk of the tool overrun occurs between the time theshut off command is given through the electrical connection 202 and thetime that high pressure air downstream of the valve 132 is exhaustedthrough the motor 134 while the amount of overrun attributable toinertia of the air tool 128 is rather insignificant at high runningtorque values because tool speed is rather slow.

The data processor 146 is shown in greater detail in FIG. 11 andconveniently comprises a Rockwell microprocessor model PPS8. For a morecomplete description of the data processor 146, attention is directed topublications of Rockwell International pertaining thereto.

The data processor 146 comprises a chassis 210 having a power source 212mounted thereon along with the signal conditioner 144, the instructionmemory and program unit 190, the data memory unit 188, themicroprocessor unit 186, the interface logic section 180, the converter150 and the logic interface amplifier section 200. The signalconditioner 144, the interface logic section 180, the microprocessorunit 186, and the data memory unit 188 are not modified in order toequip the data processor 146 to handle the calculations heretoforedescribed.

The instruction memory and program unit 190 is physically a part of thedata processor 146 and is physically modified to the extent that asuitable program has been placed therein. The initial machine languageprogram developed during the investigation of this invention containsover 7,000 instructions and, on conventional computer output paper, isapproximately 150 pages long. In the interests of brevity, economy andclarity, a FORTRAN version of the machine language program is includedwith the parent application, U.S. Ser. No. 912,151, filed June 2, 1978,and is hereby incorporated by reference. This FORTRAN program will beunderstandable to any programmer skilled in the art and may bereconverted into a machine language program either manually or by theuse of a standard language translation program. There are someinput-output functions performed in the microprocessor 186 which cannotbe converted into FORTRAN. These functions are pointed out insubroutines with comments describing what events should occur and becontrolled by the subroutines.

A second generation program has been developed. Rather than undulylengthen this specification the program instructions--found in theaforementioned U.S. patent application, Ser. No. 912,151, filed June 2,1978--are hereby incorporated by reference. Those instructions willenable anyone of ordinary programming skills to prepare a program in anysuitable language for any suitable data processor.

The interface logic and amplifier circuits 154, 200, illustratedschematically in FIGS. 12A and 12B, serve to provide interfacing of dataand control signals between the microprocessor unit 186, a conventionalteletype console (not shown), the torque and angle transducers 140, 142,and the air valve 132 controlling tool operation.

Interfacing between the teletype console and the microprocessor 186 isnecessitated by the fact that the console receives and transmits data ina serial format while the microprocessor 186 receives and transmits in aparallel format. The interface logic and amplifier circuits 154, 200include a universal asynchronous receiver transmitter circuit 212 whichreceives input data, such as a desired tension value F_(D), from theteletype console over the lines 214 in a serial or one bit at a timeformat, temporarily stores the data, and then transmits the data inparallel format over the lines 216 to the microprocessor 186. Thus ateletype console or other suitable means may provide an input 218 (FIG.10) for variable empirical parameters, desired bolt tension and thelike. Likewise, data from the microprocessor 186, which is to be printedout by the teletype console, is converted from the parallel format inwhich it is received from the microprocessor 186 over the lines 216 intothe serial format for reception by the teletype console.

Timing pulses for the control of the universal asynchronous receivertransmitter 212 as well as other components of the interface logic andamplifier circuits are provided from the microprocessor 186 over line220, the pulse train being supplied to a conventional divider circuit222 to produce a timing signal on the line 224 which is a pulse train oflesser but proportional rate to that supplied by the processor 186.Timing pulses are also provided to other components of the interfacelogic and amplifier circuit over the line 226. The microprocessor 186also provides signals over the lines 228 which signals are generated inresponse to the program to control the transmission of data to and fromthe microprocessor 186. Thus, for example, when the microprocessor 186is in condition to input data, such as the final desired torque valueT_(D), a signal is transmitted from the microprocessor 186 over thelines 228 to a gating circuit 230 to furnish control inputs at 232, 234to the universal asynchronous receiver transmitter 212. Control andstatus indication signals for the teletype console are also providedover the lines 236 and, via control conditioner circuits 238, over thelines 236 and, via signal conditioner circuits 238, over the lines 240.

FIG. 12B schematically illustrates that portion of the circuit whichprovides interfacing between the microprocessor 186, the torque andangle transducers 140, 142 and the air valve 132. Torque data from thetorque transducer 140 (FIG. 10) is converted by the analog to digitalconverter 150 into twelve digit binary signals transmitted on the line156. The particular microprocessor employed is, however, only capable ofreceiving an eight digit input. In order to permit transmission oftorque data to the processor, a multiplexing arrangement is provided.Thus, the twelve digit output of the analog to digital converter 150 issupplied, through logic level buffers 242, 244 to a pair of steeringgates 246, 248, the first four digits being supplied to the first inputsa of the gate 246 while the second four digits are supplied to thecorresponding first inputs a of the gate 248. The final four digits aresupplied to the second inputs b of the gate 246. The correspondingsecond inputs b of the gate 248 are connected to ground, supplying aconstant zero input. The eight line output 250 of the steering gates246, 248 provides the torque data input to the microprocessor 186. Thegates 246, 248 are controlled by signals on the lines 252, 254 to firstpass the a input signals, i.e. the first eight bits of the torquesignal, to the output lines 250 followed by the b input signals, i.e.the final four bits and four zeros. In addition to being supplied to thesteering gates 246, 248, the torque data transmitted on lines 156 isalso temporarily stored in the registers 256, 258, 260. These registersnormally store the current torque value received from the analog todigital converter 150. A hold signal furnished by the microprocessor 186over the line 262 actuates a latching circuit 264 to temporarily freezethe registers 256, 258, 260 permitting the torque values stored thereinto be read over the lines 266. This arrangement permits reading of thetorque data into the microprocessor 186 while updated torque data isbeing supplied from the analog to digital converter 150 without thedanger of inadvertently reading into storage a data value which is amixture of old and updated values.

The analog to digital converter 150 supplies an end of conversion signalover line 268 which signal is supplied to the latching circuit 264 overthe line 270 to reset the circuit 264 when transmission of a torquevalue has ended permitting updating of the registers 256, 258, 260. Itshould be noted that the analog to digital converter 150 is under thecontrol of the microprocessor 186. Thus the microprocessor 186 providesan enable signal over the line 272 and a convert signal over the line274 to a gate 276 which also receives, over a line 278, a tool rotationindicating signal, the origin of which will be described below. It willbe understood that the enable and convert signals on lines 272, 274 aregenerated in response to the program controlling the microprocessor 186.The output of the gate 276 provides a start conversion signal to theanalog to digital converter 150 over the line 280.

As mentioned previously, the steering gates 246, 248 receive controlsignals over the lines 252, 254. These control signals are generated bya pair of gating circuits 282, 284. The gating circuit 282 is responsiveto the end of conversion signal from the analog to digital converter 150on the line 268 and an enable signal on the line 286 which signal isderived from the enable signal supplied by the microprocessor 186 overthe line 272. The gating circuit 282 provides an input to the gatingcircuit 284 which also receives a signal over the line 288 from themicroprocessor 186 in the form of a reponse back signal indicating thatthe previous data has been loaded into the microprocessor memory. Inaddition to controlling the steering gates 246, 248, the gating circuit284 furnishes a data ready signal on the line 290 to the microprocessor186. A further input 292 is provided for the logic gating circuit 282.The function of this input is to supply an event market to memory.

The circuitry of FIG. 12B also provides interfacing between the angletransducer 142 and the microprocessor 186. The output signals of theangle transducer 142, in the form of sine and cosine signals aresupplied over the line 158 to a converting circuit 294 which, inresponse to the transducer signals, generates an output pulse for eachdegree of rotation of the tool. This pulse signal on the line 296provides the tool rotation indicating signal on the line 278 and alsoprovides an input to a gating circuit over a line 298. The gatingcircuit 300 also receives an input signal from the microprocessor 186over the line 302. This latter signal is present during the tool onperiod and goes off simultaneously with the tool off signal. The output304 of the gating circuit 300 provides an input to the microprocessor186 in the form of a pulse train with one pulse for each degree of toolrotation. The portion of this signal occurring after the input signal onthe line 302 has been removed is a measure of the degree of tooloverrun.

Also included in the interface logic and amplifier circuits is a resetcircuit 306 connected at 308 to a reset switch and providing outputsignals on lines 310, 312 which serve to reset various of the circuitcomponents when the system is turned on. Signal conditioner circuits arealso provided, with the circuits 314 providing interfacing between themicroprocessor 186 and external controls for reset, gain, internalcalibration and external calibration while the circuit 316 serves tointerface the tool on signal from the microprocessor 186 over the line318 with a solid state relay controlling the air valve 132, the outputsignal being provided over the line 320. A further circuit 322 isconnected to a single pole double throw external switch 324 serving asan emergency or panic switch. The output 326 of the circuit 322 suppliesan interrupt signal to the microprocessor 186.

The components illustrated in FIGS. 12A and 12B are more completelyidentified in Table I, below:

                  TABLE I                                                         ______________________________________                                        Identification or                                                             Standard Parts No.     Number                                                 ______________________________________                                        SN74LS04               1                                                      SN7474L                3                                                      SN7400L                5                                                      SN741QL                7                                                      SN7402L                9                                                      Resistor Pack, 4.7Kohms                                                                              11                                                     Potentiometer, 1Kohms  13                                                     72747, Texas Instruments                                                                             15                                                     Diode, 1N914           unmarked                                               SN7404L, inverter      unmarked                                               SN7437L                17                                                     Transistor             unmarked                                               SN74157L               246, 248                                               SN7496L                256, 258, 260                                          SN74161L               21                                                     Resistor Pack, 15K ohm 23                                                     SN7420L                25                                                     SN7442L                27                                                     TR1602                 212                                                    Transistor 2N2905      29                                                     Resistors 33, 620 have 1/2 watt rating                                                               unmarked                                               ______________________________________                                    

The number adjacent each resistor is the resistance in ohms. Allresistors except 33, 620 have 1/4 watt ratings. The number adjacent eachcapacitor is the capacitance in microfarads. The symbol "v" is used todesignate that the particular lead is connected to a 5 volt buss througha resistor, e.g. of 1000 ohm capacity, to prevent damage to thecomponent. The symbol "POR" is used to designate "power on reset" whichmeans that power stays on about 1/2 second.

Although the computer program and the circuitry of the interfaceamplifier section 200, previously described, are designed to activate aconventional teletype console in order to enter different values for theempirically determined parameters and to obtain a printed readout ofcertain calculated values such as the tension at the mid-point stop 62,it is apparent that the details thereof can be adapted to manipulate adisplay panel 204 as shown in FIG. 13. The display panel 204 ispreferably located within view of the tool operator and comprises a basesection 332 supported in any suitable fashion having a first group ofsignal lights 334, 336, 338, 340 indicating features of the joint 138.The signal light 334 indicates that the final desired tension valueF_(D) has been reached or that the final calculated tension valueF_(final) is within an acceptable range. The signal light 336 indicatesthat the joint has experienced nonlinear strain. The signal light 338indicates that the final calculated tension value F_(final) is in anunacceptable range. With the lights 334, 336 lit, the deduction is thatnon-linear strain has occurred but that F_(final) is acceptable. Withthe lights 336, 338 lit, the deduction is that non-linear strain hasoccurred but that F_(final) is not acceptable. The light 340 isenergized when the fastener exhibits a low tension rate as pointed outby the ratio of TR_(a) /TR_(b).

The display 204 also provides another group of lights 342, 344, 346indicating quality control features. The light 342 is normally energizedwhen the frequency of non-linear strain detection is minimal while thelight 344 is energized when the frequency of non-linear strain detectionis too high as pointed out in equation (79). The light 346 is energizedwhen the final calculated tension F_(final) differs significantly fromthe final desired tension value F_(D) as pointed out by equation (90).It will be evident that additional lights may be provided to signal thatother quality control procedures have indicated that the joint issubnormal. In the alternative, a single light may be used to signaljoint abnormality and the microprocessor arranged to deliver a signal toanother computer for record keeping purposes.

The display 204 also comprises a third group of lights 348, 350, 352indicating tool operating features. The light 348 indicates that thetool is functioning normally. The light 350 is energized when the ratioδα/δα_(p) is too small or when the frequency of low ratio values becomesignificant. Similarly when the ratio of δα/δα_(p) is too large, or whenthe frequency of high ratio values becomes significant, the light 352 isenergized.

EXAMPLES

A typical fastener system for use with this invention may comprise5/16", 24 threads/inch, SAE grade 8 nuts and bolts. With this fastenerpair and the modified Rockwell 63W air tool, the following values werefound for the empirically determined parameters:

    ______________________________________                                        FR.sub.1                                                                           = 47 lb/degree                                                                            n     = 14     r   = 1.12                                    T.sub.o                                                                            = 54 ft-lb  F.sub.M                                                                             = 2900 lb                                                                              a   = 11.6 degrees/                                                                 ft-lb                                   F.sub.L                                                                            = 1000 lb   c     = -52.3  T.sub.1                                                                           = 5 ft-lb                                                          degrees                                              α.sub.d                                                                      = 68 degrees                                                                              N.sub.k                                                                             = 0.80   R   = 0.93                                    T.sub.os                                                                           = .4 ft-lb  α.sub.y                                                                       = 12 degrees                                                                           K.sub.o                                                                           = .21 ft-lb/                                                                    degree                                  α.sub.or                                                                     = 20 degrees                                                                              α.sub.K                                                                       = 9 degrees                                                                            Δα                                                                    = 3 degrees                               ______________________________________                                    

Using these parameters and the described fasteners, which have a griplength of 2.44", and having a cadmium dichromate coating, the followingdata was developed using part of the technique here disclosed. Thestiffness of the load washer used to measure tension directly was a5×10⁶ lb/in and the clamped pieces were hardened steel. In running thetests reported in the following table, the angle option was used andexecution was within +2 to -1 degrees, which corresponds to +104 to -52pounds tension. The overall instrumentation repeatability and linearity,including the tension probe and the torque transducer, is estimated at4%. The tension value reported in the second column was recordedapproximately 15 seconds after the tool stopped. This is believed toinvolve a relaxation in the joint amounting to 1-2% of the recordedtension value.

A statistical analysis of the data gathered on the twenty fastenersreported in Table II shows that the partial technique of this inventionacts to control tension to within ±11.1% of the desired value in 99 outof 100 cases, or within 2.58 standard deviations. It should bethoroughly understood that the above data was taken with a program whichdoes not include a number of features disclosed herein, including (1)the use of a second calculation for TR and α_(origin) ; (2) theprovision of yield detection and shut off in response thereto; (3) theuse of a curvature check of torque rate in the region where TR iscalculated in order to identify and reject low tension rate fasteners;(4) the adjustment of the final tightening parameter for the effects ofprevailing torque; and (5) the use of the quality control proceduresdisclosed herein which were not disclosed in copending application Ser.No. 712,554. The effect of these additions to the program is, of course,somewhat speculative. It is believed, however, that the inclusionthereof will reduce scatter still further.

                                      TABLE II                                    __________________________________________________________________________                                           Exact                                                    Final Angle From                                                                    Exact α.sub.T.sbsb.1                                                             Torque                                               LRM Set for 6,200                                                                             5 ft-lb  for 6,200 lb                                                                        for 6,200 lb                           Run No. F.sub.final, lb                                                                         T.sub.final, ft-lb                                                                  α.sub.T.sbsb.1, deg                                                              Tension                                                                             Tension                                                                             Condition                        __________________________________________________________________________    1       6355      28.91 108      105   28.22 As received                      2       6179      32.33 109      109   32.44 As received                      3       6517      34.00 107      101   32.18 As received                      4       6356      27.61 107      104   26.93 As received                      5       6274      28.23 105      104   27.90 As received                      6       6147      30.65 108      109   30.91 As received                      7       6221      28.91 106      106   28.81 As received                      8       6205      30.77 108      108   30.75 As received                      9       6151      28.85 102      103   29.08 As received                      10      6742      31.02 109      99    28.37 As received                      11      6377      16.38 90       87    15.93 Lubricated with SAE 10 oil       12      6706      18.05 96       87    17.18 Lubricated with SAE 10 oil       13      6407      16.81 100      96    16.27 Lubricated with SAE 10 oil       14      6103      12.16 70       72    12.35 Lubricated with SAE 10 oil       15      6045      15.14 88       91    15.53 Lubricated with SAE 10 oil       16      6030      16.00 87       90    16.45 Lubricated with SAE 10 oil       17      5634      14.64 84       95    15.59 Lubricated with SAE 10 oil       18      5891      15.20 83       89    15.73 Lubricated with SAE 10 oil       19      6618      17.68 91       83    16.88 Lubricated with SAE 10 oil       20      6381      16.56 91       88    16.09 Lubricated with SAE 10 oil       Average 6267      21.31 97.5     96.3  22.68                                  Observed                                                                      deviation from                                                                        +7.8      +59.5 +11.9    +13.2 +43.0                                  Avg. %  -10.1     -42.9 -28.2    -25.2 -45.5                                  One std.                                                                      deviation, %                                                                          4.3       --    --       10.6  31.9                                   of Avg.                          8.4                                                                           on tension                                   __________________________________________________________________________

With the same joint and tool, the use of a torque control method wouldhave to produce an average final torque of 22.68 ft-lbs to achieve anaverage final tension value of 6267 pounds. The observed deviations fromaverage is +43.0 to -45.5%. Thus the torque control method would haveproduced a tension scatter of ±82.3% of the desired value in 99 out of100 cases, assuming that the bolts would have been capable of acceptingany tension. In reality, 10.4% of the bolts would have ruptured,producing no tension at the termination of tightening. Another 14.7% ofthe bolts would terminate in the plastic zone, i.e. past the yieldpoint.

With the same joint and tool, the use of a turn-of-the-nut method wouldhave to advance the nut 96.3° from a threshold torque of 5 ft-lbs toachieve a final tension value of 6267 pounds. The observed deviation is+13.2 to -25.2%. Thus, a turn-of-the-nut method would have produced atension scatter of ±21.7% of the desired value in 99 out of 100 cases.It is interesting to note that the selection of 6200 pounds for a bolthaving an elastic limit of 6950 pounds appears to be optimum becauseonly about 0.6% of these bolts would end up in the plastic zone.

In another test on the same joint, the selected final tension F_(D) was90% nominal proof or 6300 pounds. In this test, such refinements as asecond pass for the determination of TR and α_(origin) was used, anon-linear strain procedure and the remaining quality control procedureswere available. To obtain independent tension values, a load washer wasincorporated into the joint. The load washer was carefully calibratedfor mean setting and reading scatters were measured under the same loadcondition existing in the joint. Table III shows the experimentalresults. The data reported excludes any abnormal joints indicated asunacceptable by the system. Accordingly, any defective joint that wouldhave passed a torque strategy or a turn-of-the-nut strategy is excludedeven though conventional systems would not have rejected thesefasteners. Thus, the reported data on torque control and turn-of-the-nutstrategies are better than would be expected in practice. The reportedresults are corrected for load washer scatter of approximately 1.8%, onestandard deviation.

                  Table III                                                       ______________________________________                                        Tension and Torque Scatter                                                    One Standard Deviation                                                                Tension Scatter, %                                                                             Torque Scatter                                       Lube Condition                                                                          LRM        T-O-T-N     at 6300 lbs, %                               ______________________________________                                        dry       2.2        6.4         18.5                                         oiled     2.4        5.0         13.8                                         mixed     2.6        8.2         29.9                                         ______________________________________                                    

Although the data of Table III appears to be substantially differentthan the data of Table II, the major difference lies in the adjustmentin Table III of the load washer error of 1.8%, one standard deviation,whereas this adjustment has not been made in Table II.

It has been learned that torque scatter at constant tension is quitedifferent from tension scatter at constant torque. Whereas torquescatter has a normal distribution, tension scatter at constant torquehas a shifted or unsymmetrical distribution. The mixed lubricationcondition, which involves the largest variation in friction, has beenchosen to show the expectations in achieving tension control withvarious strategies. Referring to FIG. 14, the probability distributionsin finite tension bands are illustrated. It will be apparent that thetechnique of this invention is substantially superior to the torquecontrol and turn-of-the-nut strategies of the prior art.

ANALOG EMBODIMENT

Referring to FIG. 15, there is illustrated another device 354 forimplementing the technique of this invention. The basis of this approachis equation (7) where the value of dF/dα indicates the tension rate.Rewriting equation (7), ##EQU32## If d/dα log T can in some fashion bedetermined, F in equation (99) can become the final desired tensionvalue F_(D) or the tension value F_(so) at the point of shut off commandwhile dF/dα is an empirically determined tension rate FR₃ which is anappropriate average of FR₁ and FR₂ over the angle interval in question.It will be apparent that ##EQU33##

As suggested in FIG. 15, the analog device 354 includes an angular speedpickup 356 of any suitable type, such as a tachometer, for continuouslysensing a value for dα/dt, which is the speed the fastener is beingtightened.

A torque transducer 358 continuously senses the value of running torqueT. The transducer 358 may be of the same type as the transducer 140. Alogarithmic amplifier 360, such as is available from Analog Devices,Inc., Norwood, Massachusetts, under the designation of LogarithmicAmplifier, Model 755, is connected to the torque transducer 358 by asuitable connection 362. The logarithmic amplifier 360 continuouslyconverts the sensed value of running torque T into a continuous signalrepresentative of log T.

A time differentiating device 364 is connected to the logarithmicamplifier 360 by a suitable lead 366 and continuously differentiates thesignal from the logarithmic amplifier with respect to time in order toobtain the differential of the logarithm of running torque d/dt log T.The time differentiating device 364 may be of any suitable type, such asan operational amplifier 368 in parallel with a capacitor 370. Asuitable operational amplifier is available from Analog Devices, Inc.,Norwood, Massachusetts, under the designation Operational Amplifier,Model 741.

The signal from the time differentiating device 364 is delivered througha lead 372 to a low pass filter 374 which acts to smooth out the signalfrom the time differentiating device 364 thereby removing some of thenoise inherent in the torque signal from the transducer 358.

The angular speed pickup 356 and the low pass filter 374 are connectedby suitable leads 376, 378 to an analog divide device 380 such as may beobtained from Analog Devices, Inc., Norwood, Massachusetts under thedesignation Divide Module 463B. The leads 376, 378 are connected to thedivide device to produce an output signal along a lead 382 consisting ofthe ratio ##EQU34## As indicated in equation (100), this signal isrepresentative of d/dα log T. When the value of

    d/dα log T≦FR.sub.3 /F.sub.so, when T≧T.sub.1 (101)

where F_(so) is the tension value in the bolt at the time of shut off,and T₁ is an early predetermined torque value, e.g. about 20-30% of theaverage final torque, the tool is commanded to shut off. It will beevident that the threshold may be measured in terms of angle, e.g. whereα>α₁, rather than torque.

Because the tool will overrun after shut off, the value of F_(so) isselected so that average tool overrun advances the fasteners to thefinal desired tension value F_(D). The average tool overrun may bedetermined empirically or from

    ΔF.sub.so =(dα/dt).sub.so (Δt)FR.sub.3   (102)

where (dα/dt)_(so) is the average speed of the tool at shut off, ΔF_(so)is the average additional tension due to overrun, and Δt is the timedelay between the giving of the shut off command and the closing of theair valve. Thus,

    F.sub.so =F.sub.D -ΔF.sub.so.                        (103)

Because F_(so) and FR₃ are assumed to be a constant, the ratio of FR₃/F_(so) is obviously constant. Thus, a constant signal representative ofFR₃ /F_(so) is placed on a lead 384. The leads 382, 384 are connected toanother divide device 386. When the output signal from the divide device386 on a lead 388 becomes unity, an amplifier 390 is triggered toenergize a solenoid catch 392 to allow the solenoid spring (not shown)to close the air valve.

Although the analog device 354 of FIG. 15 is not believed to have theaccuracy of the digital device 126, it is apparent that it has theadvantage of simplicity, both physical and operational. The analogdevice 354 operates closer to the theoretical basis of the invention andcontains fewer assumptions and simplifications. Some of thedisadvantages of a simple analog device, such as the inability to varythe overrun prediction and the noise reduction in the filter 374, arecapable of being surmounted by more sophisticated analog techniques aswill be apparent to those skilled in the art.

As heretofore disclosed, the analog device 354 is designed to deliver arunning torque signal T which is converted into a signal representativeof log T which is then differentiated with respect to time to give d/dtlog T. As explained previously, it is desirable to adjust the runningtorque value T by deducting the values of offset torque T_(os) andprevailing torque T_(pv). It will be appreciated that this can bereadily accomplished by suitable analog devices placed in the connection362 between the torque transducer 358 and the log device 360.

As will be apparent to those skilled in the art, the technique of thisinvention can be used to monitor other tightening strategies therebydetermining the accuracy thereof in tightening fasteners to a finaldesired stress value. This may readily be accomplished by modifying theamplifier section 200 in order not to manipulate the air valve solenoidin response to the tightening parameter.

Although the invention has been described in its preferred forms with acertain degree of particularity, it is understood that the disclosure ofthe preferred embodiments has been made only by way of example andnumerous changes in the details of construction, combination andarrangement of parts, and mode of operation may be resorted to withoutdeparting from the spirit and scope of the invention as hereinafterclaimed. It is intended that the patent shall cover, by suitableexpression in the appended claims, whatever features of patentablenovelty exist in the invention disclosed.

I claim:
 1. Apparatus for tightening a fastener to a stress value belowthe yield point thereof, comprisinga tightening tool for applying torqueand imparting rotation to the fastener; means for developing a signalrepresentative of the torque being applied to the fastener and fordeveloping a signal representative of rotation of the fastener; meansfor determining, from the torque and rotation signals, an average torquerate over an angle increment of at least 10% of the angular distancebetween the origin of stress in the fastener and the proof load of thefastener in a region where the torque-angle curve is substantiallylinear; means for generating a signal epresentative of a theoreticalline parallel to the average torque rate; and means for terminatingtightening in response to non-linear strain prior to the onset of yieldof the fastener when a comparison of the torque and angle signals withthe theoretical curve signal indicates that the instantaneoustorque-angle gradient is decreasing.
 2. A process of tightening athreaded fastener to a stress value below the yield point thereof,comprisingapplying torque and imparting rotation to the fastener;sensing torque and rotation and generating signals representativethereof; calculating an average torque-angle gradient from the torqueand rotation signals over an angle increment of at least 10% of theangular distance between the origin of stress in the fastener and theproof load of the fastener in a region where the torque-angle curve islinear; generating a signal representative of a theoretical lineparallel to the average torque-angle gradient; and developing a controlsignal prior to the onset of yield in the fastener when a comparison ofthe sensed torque and rotation signals with the theoretical line signalindicates that the instantaneous torque-angle gradient is decreasing.